laid down their arms.
"Their goal is to turn Donbass (east Ukraine) into Somalia. I will not let anyone do this to our state."
Sunday's vote was seen as the most important since Ukraine's independence in 1991 as it fights to stay united and avert economic collapse after years of Soviet-era mismanagement and rampant corruption.
But the insurgency, which has already cost at least 150 lives, thwarted polling in much of the east and rebels have defiantly refused to recognise the result.
Russia, threatened with more Western sanctions if it meddled further in Ukraine after its seizure of Crimea in March, had said it was willing to work with the new leader.
"We are ready for pragmatic dialogue, on an equal footing, based on respect for all agreements, in particular in the commercial, economic and gas spheres," Lavrov said Monday. "We respect the result of the choice of the Ukrainian people."
On Tuesday, however, Lavrov said that a visit to Moscow by the new president was "not being considered."
Poroshenko also said he was ready to "engage" with the Russian leadership and was optimistic a meeting could be arranged with President Vladimir Putin soon.
Analysts see Poroshenko's emphatic victory as a first step in trying to restore stability but, said Holger Schmieding of Berenberg Bank: "That does not end the conflict in Ukraine."
Observers with the Organisation for Cooperation and Security in Europe said the election "largely upheld democratic commitments" and provided the new leader with legitimacy.
US President Barack Obama praised "courageous Ukrainians" for voting in the face of the militant threat and said Washington looked forward to working with the new president.
The ballot was called after pro-Russian president Viktor Yanukovych -- his corruption-stained regime long a source of discontent -- was ousted in February in the bloody climax of months of protests sparked by his rejection of closer EU ties.
Putin responded by seizing Crimea and threatening to invade the rest of Ukraine to "protect" the country's ethnic Russian community.
But Russia said last week it had started withdrawing from Ukraine's border around 40,000 soldiers whose presence had raised deep Western suspicions.