He said one service member was killed and 17 wounded in the previous 24 hours, and that a military jet was damaged.
There was no comment on any casualties from the rebel side.
Near the village of Karlovka, 30 kilometers (20 miles) northwest of Donetsk, residents told The Associated Press that government forces and rebels began firing heavy weapons at each other across a bridge early Tuesday, just hours after the cease-fire expired.
"There was shooting near the water. Even the water was splattering," said Inna Vladimirovna, who gave only her name and patronymic, fearful of being identified. "We know when they are just shooting to scare and when they are shooting to kill."
Ukrainian troops appeared to score some success Tuesday, with Poroshenko congratulating them on dislodging rebels from one of the three checkpoints on the border with Russia that the separatists had seized.
European leaders have been pressing Putin to persuade the rebels to lay down their weapons. The West has accused Russia of fomenting the rebellion with troops and weapons.
Russia has rejected those claims, saying that Russians who crossed into the east to fight with the rebels were private citizens. It says its influence with the rebels is limited and urges the Ukrainian government to negotiate directly with them.
Putin warned Tuesday that by ending the cease-fire, Poroshenko had made himself politically responsible for the fighting that began months before he was inaugurated in early June.
Over the last two days, Poroshenko held four-way phone talks for hours with Putin, German Chancellor Angela Merkel and French President Francois Hollande but said the rebels' failure to meet his conditions made it impossible to extend the cease-fire.
On Wednesday, foreign ministers of France, Germany, Russia and Ukraine are set to meet in Berlin to continue searching for a settlement.
In Brussels, the European Union's 28 governments decided Tuesday they were not ready to hit Russia with a new round of sanctions over Ukraine and put off a decision until Monday, according to an EU official.
The sanctions would target those responsible for fomenting unrest in eastern Ukraine, according to a diplomat from a major EU country, and could include travel bans and asset freezes for both individuals and companies. The EU has so far sanctioned only individuals.
Both the EU official and the diplomat spoke on condition of anonymity because they were not allowed to discuss the closed-door talks publicly.
Associated Press writers David McHugh in Kiev, Ukraine, Juergen Baetz in Brussels, Vladimir Isachenkov in Moscow and Edith Lederer at the United Nations contributed to this report.