"We will attack, we will free our land," BBC quoted Poroshenko as saying. The 10-day ceasefire between the Ukrainian authorities and the militants was due to end on Monday evening.
Porsoshenko said that the chance for peace was lost because of the continuous criminal activities of the pro-Russian militants.
The Ukrainian authorities and the militants have blamed each other for violation of the truce.
The militants continue to occupy key buildings in towns and cities across the east region.
Separatist leaders in Donetsk and Luhansk have declared independence.
European leaders and the US have urged Russia to use its influence in eastern Ukraine and end the violence and have threatened to impose further sanctions against senior Russian figures and businesses.