KYIV (BLOOMBERG) - A month to the day since Vladimir Putin sent in Russian troops, Ukraine's military continues an effective resistance to the invasion and President Volodymyr Zelensky remains in office, able to join Thursday's (March 24) Nato summit by video link.

For Mr Zelensky, who reportedly warned European leaders the day after the war started that they may not see him alive again, it's a moment of vindication for his unflinching defiance of Russian power.

"It's already a month of our defence against the attempt to destroy us. Wipe us off the face of the earth," he said in an earlier video address calling for people around the world to take to the streets in a show of support for Ukraine on Thursday. "They thought Ukrainians would not fight. They were wrong."

Although Mr Putin and his Kremlin officials insist what they call a special military operation to "demilitarise" and "denazify" Ukraine is on schedule and going according to plan, events on the ground suggest otherwise.

Only one larger city, Kherson in Ukraine's south, has fallen under Russian control - and troops there have resorted to shooting at crowds who turn out daily to protest the occupation, undermining Mr Putin's case that he's liberating a pro-Russia population from fascist oppression.

The North Atlantic Treaty Organisation (Nato) estimates the death toll of Russian soldiers to be at least 7,000 and potentially closer to 15,000 since combat started Feb 24.

That's more in a month than the 6,636 personnel the US Department of Defence says it lost in 20 years of war in Afghanistan and Iraq combined.

Russia has offered only one figure for casualties, 498, some 10 days into the conflict. Thousands of civilians and Ukrainian soldiers have also perished.

More than 10 million people have been displaced from their homes in Ukraine, including over 3.6 million who have fled the country, according to UNHCR, the United Nations refugee agency.

Few paths

After four weeks of fighting there are few visible paths to quickly end the human and economic destruction of a war that's likely to have long-term ramifications not just for Ukraine but also Russia and the future stability of Europe.

It remains possible that Mr Putin will achieve many of his declared goals, including what US officials have described as Plan B - seizure of Ukraine's eastern Donetsk and Lugansk provinces, together with a land corridor from Crimea, the peninsula the Russian leader annexed in 2014, to Russia.

The immediate outlook is bleak. For Ukraine, the grinding, artillery-led war that's emerging as Russian forces dig into defensive positions outside Kyiv is destroying the nation's infrastructure and damaging the capital and other cities by the day.

The Group of Seven nations plans on Thursday to warn Mr Putin against resorting to chemical or other weapons of mass destruction to escalate Russia's stalled offensive.

Mariupol, a port city on the Sea of Azov, is being reduced to rubble with 100,000 civilians still trapped without running water, heat or food. There are no routes to resupply its defenders or any genuine prospects for its relief.

Along the eastern front in Donetsk and Lugansk, tens of thousands of Ukrainian defenders dug into trenches for the last eight years are in a precarious position that could unravel quickly, should Russian forces encircle them.

Blowback on allies

For now, leaders attending a European Union summit and the 30 member states at the Nato talks will have to figure out how to sustain Ukraine's economy and resupply its military with weaponry needed to continue fighting, while tightening the sanctions squeeze on Russia to pressure it to end the war.

That's far from a given. While sanctions are hurting the Russian economy, and Mr Putin has suffered resignations - such as the loss of his international climate envoy Anatoly Chubais, who's left the country - there are few if any signs his position is under threat.

The wide-ranging sanctions and the war are also having blowback effects on the US and its allies that could strain alliance unity in months to come, including on energy and food price inflation.

According to modelling by Bloomberg Intelligence, growth in the EU will slow by 1.6 percentage points if the conflict continues and 3.3 percentage points if it escalates. The same figures for the US are 0.5 and 0.9 percentage points, respectively.

Within Russia, access to independent and foreign media has been suppressed as the country reverts to an angry isolation reminiscent of the Soviet Union in the Cold War era.

Amid a clampdown on social media, state TV, from which most Russians get their news, has cast the conflict as a series of steady victories in a campaign mostly in eastern Ukraine to rescue Russian speakers from genocide.

Many Russians appear eager to believe this alternative version of events.

Putin's support

While there hasn't been a reliable poll since the start of the conflict, surveys done in Russia suggest public support for Putin and the war is rising.

In an attack on so-called oligarchs the US and Europe sanctioned in hopes they'd pressure the Kremlin into changing course, Mr Putin last week lashed out at "scum and traitors" that he accused of working covertly for Russia's opponents. The Russian people would "spit them out like a midge that accidentally flew into their mouths", he said.

Talks are continuing between Ukrainian and Russian negotiators in the search for a settlement, though it looks unlikely any time soon. Russia may not be able to occupy Ukraine or secure its compliance, but it retains more than enough military capacity to destroy much of the country, with just under 90 per cent of the combat power still available, according to a Pentagon estimate. It is also seeking reserves from Syria as well as at home to reboot the campaign.

The Kremlin's demands have reduced since the start of the war, in that they no longer appear to include regime change.

Yet they remain politically impossible for a Ukrainian leader to accept, not least because of a widespread belief in Ukraine that achieving an end to the war by ceding territory would likely provide only a temporary reprieve in a Russian campaign to seize control of the country that began with Crimea's loss eight years ago.