Taking the oath of office in Kiev, Poroshenko appealed to the rebels to lay down their arms, offering peaceful dialogue and immunity from prosecution to "those who don't have blood on their hands".
His inaugural address in parliament gave little sign of a quick resolution to the conflict in the east, which Ukrainian officials say has left more than 200 people dead.
He also took a firm line on Russia's annexation of Crimea this spring, insisting that the Black Sea peninsula "was, is and will be Ukrainian".
In response to Poroshenko's remarks, a rebel spokesman in the self-styled Donetsk People's Republic, which has declared independence from Ukraine and wants to unite with neighbouring Russia, told reporters the fight would continue.
"What they really want is one-sided disarmament and for us to surrender. That will never happen," said a top separatist official, Fyodor Berezin. "As long as Ukrainian troops are on our soil, I can see that all Poroshenko wants is subjugation," he said from Donetsk.
Since Poroshenko's election on May 25, government forces have stepped up what they call an "anti-terrorist" campaign against the Russian-speaking separatists in the east of the country.
The rebels have fought back, turning parts of the east into a war zone. On Friday, they shot down a Ukrainian army plane and killed a member of the interior ministry's special forces in the separatist stronghold of Sloviansk.
Fighting continued around Sloviansk yesterday and smoke could be seen rising above the surrounding forests.
Ukrainian armoured personnel carriers and military transport vehicles lined the road leading into the city, and soldiers behind concrete blocks and sandbags trained their machine guns on cars and buses driving out.
Inna, 38, was leaving by foot with her mother and grandmother, carrying bags with food, water and clothes. "We've been hiding in the cellar for three days and we finally decided to leave. There is no water or electricity," she said.
In his speech, Poroshenko said the government was prepared to talk to peaceful citizens - "clearly not with gunmen and other scoundrels" -and would offer a safe corridor for fighters who had crossed the border from Russia to go home.
Yesterday, Russian president Vladimir Putin gave an order to the Federal Security Service to strengthen protection of the country's border with Ukraine to prevent people crossing illegally.
The order came a day after Putin held talks with global leaders in France, where President Barack Obama called on him to cease support for separatists in eastern Ukraine and stop the provision of arms and material across the border.
While the Ukrainian government tightens its grip around Sloviansk, now encircled by the army, it appears to be losing ground in its easternmost region of Luhansk, where border guards have fled several bases after coming under attack.
Around 200 people protested against the presidential inauguration in the centre of the city, some laying flowers on the sun-baked sidewalk in memory of eight people killed last week.