KYIV (NYTIMES) - Russian forces opened the day on Saturday (March 12) with heavy bombardment of cities across Ukraine, including Kyiv, the capital, and the southern city of Mykolaiv, escalating the fighting in both places and raising fears that deadly ground assaults would intensify as well.

Air-raid sirens sounded in cities across Ukraine before dawn. In Mykolaiv, a port city of about 500,000 residents near the Black Sea, residents awoke to the sounds of a fierce battle between Russian forces and Ukrainians defending the city. Hours earlier, Russian shelling there hit several civilian targets, including a cancer hospital, and sent residents fleeing into bomb shelters.

The early morning fight was concentrated in the north of the city, said Colonel Sviatoslav Stetsenko of the Ukrainian army's 59th Brigade, who was stationed near the front lines.

President Volodymyr Zelensky accused Moscow on Saturday of terrorising the nation in an attempt to break the will of the people, calling the invasion  "a war of annihilation".  

Russian forces have not achieved anything resembling a strategic military victory since the first days of the war.

The Ukrainian military said on Saturday that all attempts by Russian forces to advance on any front had been stopped and that the Ukrainian forces inflicted “heavy losses in manpower and equipment”.

The claim could not be independently confirmed but was in line with analyses by the Institute for the Study of War and other military experts. Russian officials said they were having success in seizing Ukrainian military equipment, including surface-to-air missiles, and in cutting off cities in the strategic south.

The Russian assault on Kyiv appeared to be intensifying on Saturday, but attacks by Ukrainian light infantry units and Turkish-built drones continued to have some success in ambushing Russian tanks, artillery and mechanized vehicles, according to video evidence and assessments by both the Pentagon and British defense intelligence.  

For two weeks, Russian forces have failed to take the strategic southern city of Mykolaiv and, in turn, have stepped up their bombardment of civilian targets there, causing damage to a cancer hospital and sending residents fleeing into bomb shelters.

Once again on Saturday morning, residents awoke to the sounds of artillery fire and explosions.

President Vladimir Putin of Russia has demonstrated in past conflicts in Syria and Chechnya a willingness not only to bomb heavily populated areas indiscriminately but also to use civilian casualties as leverage against his enemies.

On Friday, evidence mounted that the Russian military was doing exactly that in Ukraine. A shoe factory, a psychiatric hospital and an apartment building were among the latest civilian targets hit by Russian forces, Ukrainian officials said.

Apart from the brutality of such an approach, analysts said it may reflect the mounting challenges that Russia faces, as Putin's goal of a swift, decisive victory has been slowed by logistical problems and resistance by the smaller but highly motivated Ukrainian military.

Citing Russia's second war with Chechnya and its assault on the capital, Grozny, beginning in 1999, military experts raised doubts that Russia could prevail in Ukraine relying solely on a strategy of pulverising cities and pummelling civilians.

"Grozny was the elusive target," said Dr Paul Stronski, a senior fellow with the Russia and Eurasia program at the Carnegie Endowment for International Peace. "They were able to carpet-bomb Grozny and destroy the city, but the insurgency continued." It ended 10 bloody years later.

Moving to exact a heavier economic toll in response to the assault, US President Joe Biden on Friday said the United States would join the European Union and other allies in stripping Russia of permanent normal trade relations and would take steps to bar it from borrowing money from the International Monetary Fund and the World Bank.

"Putin must pay the price," Mr Biden said, calling him an "aggressor". Mr Biden said he also planned to ban certain imports from Russia, including seafood, vodka and non-industrial diamonds, as well as American exports of luxury items such as high-end watches and luxury vehicles.

After underestimating Ukrainian resistance and overestimating the Russian military's ability to conduct a complex invasion by air, land and sea, Mr Putin was ramping up what that Russian army does best: shelling and missile strikes, according to a senior Pentagon official and other US officials.

Near the eastern town of Izyum, Ukrainian officials reported a strike on a psychiatric hospital, where 30 workers and 300 patients were in a bomb shelter. That came two days after an attack on a children's hospital and maternity ward in the besieged port of Mariupol, Ukrainian officials said.

After several quiet days in the southern port of Mykolaiv, Russian forces hit a cafe, a home and the parking lot of a large shopping centre, the regional governor Vitaliy Kim said.

Russian forces also struck Lutsk, in north-west Ukraine; Ivano-Frankivsk, in the south-west; and Dnipro, in central Ukraine, where missiles landed near a kindergarten, an apartment building and a two-story shoe factory, which broke out in flames, according to the Ukrainian military.

Across Ukraine, at least 564 civilians have been killed and 982 have been injured by Russian forces that have used heavy artillery, rockets and widely banned cluster munitions in populated areas, the United Nations said.

"Schools, hospitals and kindergartens have been hit, with hugely devastating consequences," Ms Liz Throssell, a spokesman for the UN human rights office, said in Geneva.

Russian forces have attacked at least 26 hospitals and health care facilities, the United Nations said. Those strikes have killed 12 people, including two health care workers, and injured 34, eight of them medical workers, Mr Tarik Jasarevic, a spokesman for the World Health Organisation, told reporters by video link from Lviv in western Ukraine.

The mayor of Melitopol, a small south-eastern city that was one of the first to fall to the Russians, was kidnapped by Russian forces on Friday, according to President Zelensky, who called it "a sign of the weakness of the invaders".

"We are not cooperating with the Russians in any way,” the mayor Ivan Federov had said emphatically a week earlier, when residents took to the streets in protest.  

On Friday, video was released of a man with a bag over his head being led away from a government building by Russian soldiers. Mr Zelensky, in his overnight speech, said that the man was Fedorov.

The war has left hundreds of thousands of civilians in dire conditions in besieged cities as food runs low, clean water supplies dry up and access to medical care becomes scarce. More than 2.5 million Ukrainians have fled the country in the fastest-growing exodus of European refugees since World War II, according to the United Nations.

The situation is particularly catastrophic in Mariupol, where on Friday, Mr Pyotr Andryuschenko, an adviser to Mariupol's mayor, said it was impossible to tally bodies in the streets because the bombing had not let up.

"Since 6am, there has been no break: shelling, bombardment, shelling, bombardment," he said. "The last relatively safe places in the city are being shelled, and they are shooting at residential areas."

He added: "Humanity has not yet invented a word for what Russia is doing to us."

Beyond Ukraine, the war reverberated in negotiations to revive the 2015 nuclear deal with Iran, as officials said the talks had been paused because of Russian demands that sanctions imposed on it because of the invasion exclude its dealings with Iran.

European officials expressed concern that the pause might be the death knell for efforts to bring the United States and Iran back into compliance with the deal, which limits Iran's nuclear program while lifting economic sanctions on Teheran imposed by the United States.

A deal would bring Iranian oil back on the world market at a time when Western countries are trying to wean themselves off Russian oil and gas. Those hopes have now been cast into limbo.

The Russian authorities, toughening their crackdown on dissent, began the process of banning Instagram, one of the last Western social networks operating in the country. They also opened a criminal case against Meta, parent company of Instagram and Facebook, asking a court to declare it an "extremist organisation".

While Russia was attacking a wide circle of cities on Friday, Russian and Ukrainian forces were girding for what is shaping up to be a climactic battle in Kyiv, which a Ukrainian presidential adviser, Mr Mykhailo Podolyak, on Friday called a "city under siege".

That could be a long, drawn-out fight with thousands of casualties on both sides, as well as among the roughly 1.5 million citizens remaining in the city. One Russian column approaching from the northwest was about 9 miles from the city centre, a senior Pentagon official said, while another column pushing in from the north-east was about 19 to 28km away.

A senior US official said it could take up to two weeks for Russian forces to encircle Kyiv and then at least another month to seize it, in all likelihood through a combination of relentless bombardment and what could be weeks or months of door-to-door street fighting.

And there are important differences between what took place a generation ago in Chechnya, with a population of about two million, and Ukraine, with about 44 million. The assault on Grozny took place before the social media era, and in a distant, former Soviet republic that fewer Russians thought of as part of Russia, rather than a nation portrayed in Russian state media as an inseparable part of Russia.

"It runs so much against the Russian narrative that the Ukrainians are our brothers and Ukraine is part of our history," said Dr Michael Reynolds, associate professor of Near Eastern Studies at Princeton University.

Or, as Dr Stronski said: "Kyiv is the historic birthplace of both Ukraine and Russia. It is dicier to carpet bomb a place like Kyiv or Kharkiv than it was Grozny."