The Ukrainian military admitted Tuesday that it no longer had full control over the strategic railway hub of Debaltseve, as rebel leaders claimed to have seized broad swaths of ground in street-by-street combat, including the train station.

The apparent gains in Debaltseve by pro-Russian separatists came as they and Ukrainian forces picked up the pace of their artillery battles, trading fire in areas around the city despite a 3-day-old cease-fire under which the two sides were to remove their heavy weapons from the front lines starting midnight Tuesday.

During the day, the Ukrainian military was seen and heard launching projectiles from multiple rocket launchers along a highway leading to Debaltseve, while evidence of shelling from rebel positions also was apparent, especially near a power plant outside Svitlodarsk, where one shell hit a gas pipe, causing a fiery explosion.

The worsening situation posed a critical challenge to the continued viability of the cease-fire, which never really took effect around Debaltseve, although it was observed at other points along the front lines since going into effect Sunday. And before the fighting in and around Debaltseve potentially unravels the fragile peace elsewhere in eastern Ukraine, the government faces the question of to do about the 5,000 troops all but trapped in the contested city.

Over the past several days, separatist forces have effectively encircled Debaltseve, blocking it on all sides except along the highway leading to pro-Ukrainian territory. But soldiers who escaped described that road as all but impassable, because the rebels occupy positions on either side.

Although Ukraine has gone through a series of large-scale mobilizations since it began fighting against separatists in the east, 5,000 soldiers is still a measurable percentage of the Ukrainian army's ready fighting force. A year ago, before the war commenced, it would have been almost the entire combat-ready force of the country, according to estimates the defense minister provided to parliament at the time.

Pro-Russian rebel leaders have offered the troops a way out only through surrender. On Tuesday, they claimed that at least dozens of pro-Kiev soldiers were voluntarily giving up their positions and weapons.

"The Debaltseve 'boiling pot' is closed," Luhansk rebel leader Igor Plotnitsky said. "It is Ukraine who cannot, and does not want to, recognize this."

But Col. Andriy Lysenko, a spokesman for the Ukrainian National Security and Defense Council, denied that any Ukrainian soldiers had surrendered. He also accused the separatists of capturing a group of Ukrainian soldiers who were trying to deliver supplies to encircled troops when they ran out of ammunition -- but he did not say how many had been taken prisoner.

Trapped soldiers and some of those who managed to break out described the situation on the ground as a special brand of hell. The protracted crisis has inspired leaders of some of Ukraine's volunteer battalions to plead with Kiev to adopt a new strategy.

Semyon Semenchenko, the head of the pro-Kiev Donbas battalion, many of whose fighters are in Debaltseve, called on military and political leaders to take "decisive actions" to free the soldiers, adding that any delays could be "very costly" and that simply trying to hold their position "could lead to disaster."

Semenchenko suggested that it might be time to give up trying to hold Debaltseve.

"It is necessary to save the core of the army," he said. "Territory we can always get back."

The situation in Debaltseve has led Ukrainians to draw likenesses between the soldiers' ongoing predicament there and the summer siege of Ilovaysk, during which the Donbas battalion claimed 1,000 soldiers had died.

"We have had Ilovaysk. Now we have Debaltseve," Aleksander Chelobitchenko, a senior lieutenant on the Ukrainian side of the Joint Control Commission, a combined Ukrainian-Russian observational team based in Soledar, said Tuesday. "If you keep cutting the branches off a tree, eventually the tree will die. This is very bad, to lose all this."

But the sum total of the stakes of losing Debaltseve is not just in the number of soldiers' lives hanging in the balance, Chelobitchenko said.

"It's not just the people. It's also the equipment and the weapons there," he said. "If one side takes over the equipment, they can turn it against the other side."

The equipment and weapons that could trade hands if Ukrainian troops surrender or lose would be a significant gain for rebel forces, even if Ukrainian leaders are still regularly pleading with their Western allies, especially the United States, to supplement their combat efforts with lethal military aid. They need it, Ukrainian leaders insist, to face up against separatists that Kiev and its allies believe are being directly supplemented by Russian troops and weapons.

Russia has routinely denied direct involvement in the conflict. On Tuesday, Russian President Vladimir Putin pointed a finger in the opposite direction. Asked during a visit to Hungary how Russia would respond to a U.S. shipment of lethal arms to Ukraine, Putin said that "these weapons are available now." He also said that no matter what weapons were introduced in the conflict, "the number of victims can certainly increase."

The Obama administration has said repeatedly that no decision has been made to send lethal aid to Ukraine. A spokesman for the National Security Council said in Washington Tuesday that the policy was still intact and that the administration had "no idea what Putin is referring to."