DNEPROTROVSK REGION, UKRAINE - After Ukraine's stunning offensive in its north-east drove Russian forces into a chaotic retreat and reshaped the battlefield by hundreds of miles, Ukrainian leaders Monday were weighing critical gambles that could determine the near-term course of the war.

Stretching the Ukrainian forces - a military still much smaller and far less equipped than its Russian foe - too far could leave the troops vulnerable to attack. Moving too slow, or in the wrong place, could leave an opportunity squandered. And waiting too long could allow the front lines to freeze as winter sets in.

By expelling Russian troops from a large slice of strategic territory in the north-eastern Kharkiv region, Ukrainian forces are now positioned to make a move on the Donbas, the industrialised eastern territory that President Vladimir Putin of Russia has made central to his war aims.

Just before flooding troops across the border in February, Mr Putin declared the Donbas independent from Ukraine, and he held up the region's sovereignty as a key justification for the invasion.

Russia now has control of nearly 90 per cent of the Donbas, where its military shifted much of its focus after a staggering defeat around the Ukrainian capital, Kyiv, in the spring. If Ukraine were to retake even a part of the region, it would be an embarrassing blow to the Kremlin.

On Monday, the Ukrainian military claimed to have advanced over the past day into an additional 20 Ukrainian towns and villages in the Kharkiv region that had been under Russian control, adding to the hundreds of square miles it has retaken in the north-east.

It also said it had recaptured nearly 200 square miles (518 sq km) in the southern Kherson region in recent days, as its forces try to cut off thousands of Russian forces stationed west of the Dnieper River.

The military's assertions could not be independently verified, but Western analysts, including at the Pentagon, said that the Ukrainians were overall making gains as quickly as Russian forces were falling back.

But Ukraine faces potentially serious pitfalls if it pushes any farther.

Any future advances would mean that Ukrainian forces would further extend their supply lines, straining convoys of fuel, ammunition and reinforcements as they have to move farther away from their established logistics hubs.

That could leave Ukrainian units vulnerable, said Professor John Blaxland, a security and intelligence studies expert at the Australian National University in Canberra. Although he added that a Russian counterattack was "not necessarily going to happen," in part because the morale of Moscow's troops appears to be foundering.

Russian officials face their own hard questions, especially with a growing backlash to their "special military operation" from pro-war voices at home. Russia's military leaders, analysts say, will have to take a clear-eyed look at the reality of their forces' current conditions - depleted and demoralised in some areas - to determine how much of Moscow's goals they can accomplish in the coming months, if any.

They will also have to contend with the rigid structure of Russia's military and, ultimately, the decisions of Mr Putin, who has resisted mobilising a national draft and sought to preserve a sense of normalcy inside Russia.

The current Ukrainian offensive "was a rapid breakthrough designed to take advantage of favourable positions and thinly manned Russian defences," said Mr Michael Kofman, the director of Russian studies at CNA, a research institute in Arlington, Virginia.

With momentum currently on Ukraine's side, the recent string of victories around the country's second-largest city, Kharkiv, means Ukrainian troops are positioned to make gains farther east - before Russian forces can retrench on new front lines.

"Ukraine now has options to exploit momentum" in the Donbas, Mr Kofman said. Russian forces, he added, "will be on the defensive for the foreseeable future."

Ukraine's ability to recapture roughly 1,000 square miles around Kharkiv in a matter of days was largely predicated on a Russian retreat, as Moscow's forces withdrew to avoid encirclement and isolation, especially near the strategically important city of Izium.

The Russian pullout from the Kharkiv region and Izium, a railway hub, has left the Ukrainians with the "ability to shift quickly" elsewhere in the country, Mr Kofman said.

He also noted Ukraine's troops have an advantage in manpower and the ability to conduct "operations along more than one axis," referring to a separate offensive taking place in Ukraine's south, near the port city of Kherson.

Along Ukraine's newly established front in the Kharkiv region, Ukrainian troops not only have to prepare for future advances but also fortify their own gains.

Securing territory is a resource-intensive challenge in its own right. In recaptured towns and villages, Ukrainian units have to sweep for explosives, including inside abandoned Russian equipment, and look for potential saboteurs. Once those tasks are complete, emergency services such as police and bomb disposal crews can arrive.

Russian troops appear to have left a large amount of equipment behind, as they did during their hasty retreat from Kyiv.

One soldier familiar with the battle said that one unit that took part in the offensive around Kharkiv is already known to have captured so much Russian equipment, including tanks and ammunition, that other units are looking to use it to fill their own supplies.

But Ukraine's window of opportunity to take advantage of Russia's degraded morale and pell-mell retreat is quickly closing.

Every day that passes, Russian forces have time to dig in and gather reinforcements, drawing new defensive lines and preparing to return to the months-long status quo of a grinding artillery battle. Pro-Russian social media accounts have shown images of Russian and pro-Kremlin Chechen forces mustering for deployment in Ukraine or headed to the front.

Russia retains an advantage in weapons and supplies, and Mr Putin has over the course of the war shown no sign of relenting his military's assault. Last week he insisted Russia had "not lost anything, and will not lose anything," dismissing his country's casualties to that point.

With Russia's Kharkiv defences demolished and their troops redeploying elsewhere, the last remaining Russian front lines - those in the Donbas and Ukraine's south - are likely where the remainder of intense ground fighting will play out, analysts said.

But on Sunday night, Moscow demonstrated its willingness to punish Ukraine for its military successes by appearing to launch cruise missiles at power plants and their substations in the country's east.

The reminder was not subtle: Despite losing the battle, the war was far from over. NYTIMES