Ukrainian President Petro Poroshenko has ended a unilateral ceasefire with separatists in the east, saying: "We will attack, we will free our land."
Mr Poroshenko said the chance to implement a peace plan was lost because of the "criminal activities" of pro-Russian militants.
The shaky 10-day ceasefire between the Ukrainian authorities and separatist groups had been due to end late Monday.
Both sides have accused each other of violating the truce.
Interfax-Ukraine news agency quoted pro-Russian militia saying Ukrainian forces had resumed shelling the town of Kramatorsk.
"The decision not to continue the ceasefire is our answer to terrorists, militants and marauders," Mr Poroshenko said.
Earlier on Monday, the office of French President Francois Hollande said Ukraine and Russia had agreed to work together to establish a bilateral ceasefire in eastern Ukraine.
It followed talks between the leaders of Ukraine, Russia, Germany and France.
Armed pro-Russian rebels are occupying key buildings in towns and cities across the east, defying the government in Kiev.
Separatist leaders in Donetsk and Luhansk have declared independence.
However, Ukrainian troops are besieging the insurgents in several areas.
European leaders and the US have urged Russia to use its influence with the rebels to end the violence and have threatened to impose another round of economic sanctions against senior Russian figures and businesses.
There had been hopes that the ceasefire would hold after the French presidency said on Monday that Russian President Vladimir Putin and Mr Poroshenko had agreed to work on "the adoption of an agreement on a bilateral ceasefire between Ukrainian authorities and separatists".
It followed a four-way teleconference between the two men, French President Francois Hollande and German Chancellor Angela Merkel.
Mr Putin had earlier stressed the importance of extending the ceasefire, and called for the Organisation for Security and Cooperation in Europe (OSCE) to play an "active role" in monitoring a truce.
However, the OSCE earlier said it was scaling back monitoring operations and freezing deployments to Ukraine's east.