Fighting intensified in eastern Ukraine Sunday as thousands rallied for peace in Kiev. (Reuters)

Intensifying battles, mounting death tolls and new accusations of Russian interference in eastern Ukraine have marked some of the worst fighting between government troops and pro-Russian separatists since last summer, rendering a months-old cease-fire agreement effectively defunct.

The two sides have been trading heavy fire at the Donetsk airport, a prize that, though more symbolic than strategic, has been at the center of punishing recent attacks that have reduced much of the facility to rubble. Each side has claimed control of the airport at various points, and militia and army fighters there continued to launch strikes against each other over the past several days.

The Ukrainian army was attacked by “regular military formations” of the Russian army, Col. Andriy Lysenko, the Ukrainian military spokesman, said Tuesday. Ukraine’s National Security and Defense Council said Monday that Russia had sent “two battalions” — about 800 soldiers — across the border. Lysenko added Tuesday that three more battalions had approached the Russia-Ukraine border from the Russian side.

Those assertions, which could not be independently confirmed, follow months of accusations from both Kiev and NATO that Russia has been fueling the separatist uprising in eastern Ukraine with a steady stream of weapons and personnel. Russia has routinely denied such accusations, maintaining that it is Kiev that is intent on furthering the conflict.

The U.S. ambassador to Ukraine, Geoffrey R. Pyatt, bolstered Ukraine’s accusations Tuesday, saying the United States was alarmed by what he called a Russian-provoked military escalation, coupled with the arrival of large quantities of weaponry from Russian territory, according to the Russian Interfax news service. The renewed tensions have also prompted stern rebukes from Moscow, where Kremlin officials charged that Ukrainian President Petro Poroshenko dismissed a new peace plan that Russian President Vladimir Putin offered last week. It proposed that the sides in the conflict “take urgent measures to cease fire” and pull back large weapons to lines agreed upon in September.

A Ukrainian tank travels a road in the village of Tonenke, about three miles from the Donetsk airport Jan. 19, 2015. Government troops and pro-Russian separatists have recently engaged in some of their heaviest fighting since last summer. (Oleksandr Stashevskiy/AFP/Getty Images)

“It’s the biggest, even a strategic mistake by the Ukrainian authorities to use force to resolve the crisis,” Russian Deputy Foreign Minister Grigory Karasin told Interfax on Monday. “It may lead to irreversible consequences for Ukrainian statehood.”

Ukrainian leaders acknowledged that Kiev received the letter in which Putin outlined his proposals for a truce. But they denied that Ukrainian soldiers have breached the cease-fire, defending the military’s actions as legitimate responses to breaches of the cease-fire by pro-Russian rebels.

Ukrainian Foreign Minister Pavlo Klimkin told reporters Tuesday that pro-Russian separatists were “taking advantage” of the military’s compliance to seize “very substantial territory — more than 500 square kilometers.”

Putin’s proposal came as mediated talks between the sides appeared to be breaking down.

German Chancellor Angela Merkel — widely seen as Putin’s closest negotiating contact in Europe — canceled plans for a meeting involving France, Germany, Russia and Ukraine in Kazakhstan last Thursday, saying not enough progress had been made on the peace plan that rebels and Ukrainian officials agreed on in the Belarussian capital of Minsk in September. Mediated talks between representatives of the Ukrainian government and pro-Russian separatists that had been scheduled for the next day also were canceled.

A new round of talks had been scheduled for Wednesday in Berlin.

Meanwhile, Russia’s relationship with its European partners beyond talks on Ukraine continues to be tense. U.S. and European leaders say any discussion of rolling back economic sanctions against Russia over its involvement in Ukraine depends on Moscow’s support for the agreement reached in Minsk. On Monday, European Union leaders said there were no plans to ease the economic sanctions, given the situation in eastern Ukraine.

In the meantime, the death toll in the conflict zone is mounting. The United Nations estimates that more than 4,800 people have been killed in the fighting there since April.

Civilian casualties also appear to be increasing. A grenade attack was carried out against a group of Ukrainian nationalists in the government-controlled eastern Ukrainian city of Kharkiv on Monday, the same day a hospital in Donetsk was struck. Rebels said dozens more were killed or injured in Ukrainian airstrikes in Horlivka on Sunday.

Last week, 13 civilians died when a bus was shelled in eastern Donetsk — the largest single loss of civilian life since the September truce.