Poroshenko said he is in close contact with the Kiev government, and added the "anti-terrorist operation ... has finally really begun."
The Ukrainian military used fighter jets and helicopters, earlier in the week, to retake the airport in the city of Donetsk from rebels who said they suffered considerable losses in the attack.
Poroshenko added he hopes to talk with U.S. President Barack Obama next week to seek military supplies and training.
The wealthy Poroshenko easily won the May 25 presidential election on a platform of growth and a pro-Western outlook, although he said he is eager to pursue negotiations with Russian President Vladimir Putin.
"Russia's goal was, and is, to keep Ukraine so unstable that we accept everything that the Russians want. I have no doubt that Putin could, with his direct influence, end the fighting," Poroshenko said.