There were reports of heavy shooting and bombardments all across eastern Ukraine on Tuesday, including civilian casualties. Gunfire cracked in the center of the regional capital of Donetsk, where rebels and government forces fought for control of the Interior Ministry headquarters and a police building came under attack by the separatists.

In the city of Kramatorsk, to the north, four people were killed when a minibus came under artillery fire, Ukrainian news agencies reported.

In a significant victory for the government, Ukrainian forces retook control of a checkpoint at Dolzhansky, in the Luhansk region, one of three important border crossings with Russia that had been seized by rebels. European leaders demanded on Friday that the crossings be surrendered to Ukrainian authorities.

Mr. Poroshenko issued a statement congratulating his troops for reclaiming the border checkpoint. Overnight, there were reports that two explosions damaged railroad lines in the east. A television tower serving the besieged city of Slovyansk was destroyed by artillery fire. Photographs posted on the Internet showed the metal lattice of the tower reduced to a tangled pile of rubble.

The resumption of military operations was cheered by many supporters of the Ukraine government. In Kiev, Alyona Getmanchuk, the director of the Institute of World Policy, a research organization, said that by engaging in protracted peace talks even as soldiers continued to be killed, Mr. Poroshenko had failed to live up to campaign promises that he would not negotiate with terrorists and that he would swiftly crush the insurrection.

“He was elected as a crisis manager, not as a diplomat, and even before elections he said that antiterror operations should last hours, not days or months or weeks,” Ms. Getmanchuk said in an interview. “People liked it and people thought he would be very decisive and he would resolve the problem within a couple of days, maximum weeks.”

Mr. Putin, in a speech to diplomats in Moscow on Tuesday, said that he and other leaders had sought to persuade Mr. Poroshenko to continue the cease-fire during the conference call on Monday, but that the Ukrainian leader had chosen war and would now bear personal responsibility for the outcome.