Moscow said it was ready for dialogue with Petro Poroshenko but he should scale back his armed forces' campaign in the east, where pro-Moscow gunmen have declared independence in two provinces.
Ukrainians rallied overwhelmingly in Sunday's election behind Poroshenko, a billionaire owner of chocolate factories and political veteran, hoping the burly 48-year-old can rescue the nation from the brink of bankruptcy, civil war and dismemberment by their former Soviet masters in the Kremlin.
Preliminary results with about half of votes counted gave Poroshenko 53.7 percent of the vote - towering over a field of 21 candidates with enough to avert a run-off. His closest challenger, former premier Yulia Tymoshenko, secured just 13.1 percent and made clear she would concede.
In a news conference on Monday, Poroshenko made clear his most urgent task is finding a modus vivendi with the giant neighbour that has seemed poised to carve Ukraine up since a pro-Russian president was ousted in a popular revolt in February.
"I hope Russia will support efforts to tackle the situation in the east," Poroshenko said. He said he planned to meet Russian officials in the first half of June.
Poroshenko said he was ready to talk to pro-Moscow separatists who lay down their arms, but would not meet with "terrorists" who threaten the security of the state.
Ukraine's "anti-terrorist" military operation against rebels in the east would press on but must be more effective, he said. So far, Ukraine's military forces have had little success against rebels who have declared independent "people's republics" in the eastern industrial heartland.
Russian Foreign Minister Sergei Lavrov repeated a weekend promise by President Vladimir Putin that Moscow would respect the will of Ukrainians. Moscow was ready for dialogue with Poroshenko but Kiev should not step up its military campaign, Lavrov said.
Poroshenko's robust margin gives him a firm mandate, even though millions of Ukrainians were unable to vote in eastern regions prowled by armed pro-Moscow separatists.
Veteran survivor takes 'heavy burden'
Many Ukrainians clearly rallied behind the frontrunner as a way to demonstrate national unity, three months after a pro-Russian president was ousted in a popular revolt and Moscow responded by seizing the Crimea peninsula, massing troops on the frontier and expressing sympathy with armed separatists.
A veteran survivor of Ukraine's feuding political class, Poroshenko served in cabinets drawn from governments on both sides of Ukraine's pro- and anti-Russian divide, but threw his weight and money behind the revolt that brought down his Moscow-backed predecessor in February.
"He has taken a heavy burden on his shoulders," said Larisa, a schoolteacher who was among crowds watching the results on Independence Square, where pro-Western "EuroMaidan" protests ended in bloodshed in February that prompted President Viktor Yanukovich to flee to Russia. "I just want all of this to be over. I think that's what everybody wants."
In the eastern Donbass coalfield, where militants shut polling stations cutting off some 10 percent of the national electorate from the vote, rebels scoffed at the "fascist junta" and announced a plan to cleanse their "people's republic" of "enemy troops".
More than 20 people were killed in the region last week.
On Monday, the international airport in Donetsk, the biggest city of the Donbass, closed after dozens of armed separatists arrived at the terminal in the early hours to demand the withdrawal of Ukrainian troops from the area. No violence was reported.
Claiming a popular mandate for a resumption of efforts to bind the nation of 45 million into association with the European Union - a drive that triggered the whole crisis six months ago - Poroshenko said he was ready to negotiate with Putin and called Russia a vital partner. He insisted Crimea must be returned.
Eastern uprisingYet it remains unclear how the tycoon can turn firmly westward as long as Russia, Ukraine's major market and vital energy supplier, seems determined to maintain a hold over the second most populous ex-Soviet republic.
Nor is it clear that Poroshenko has new answers to resolving the uprising in the industrial east, given the weakness of his forces and the threat of Russian military intervention - a threat that has raised fears of a new Cold War, or worse, and has been met by only tentative U.S. and EU economic sanctions.
Declaring that his first trip would be to the Donbass - though quite when is unclear as it may take some time to be sworn in - Poroshenko said he was ready to negotiate with anyone, and to offer the region autonomy, Russian language rights and budgetary powers that many want in the east.
"To people who have taken up arms but are not using them, we are ready to give amnesty," he told an earlier news conference at which he fielded questions in a fluent mix of Ukrainian, Russian and English. "As for those who are killing, they are terrorists and no country in the world conducts negotiations with terrorists."
Poroshenko can be sure of a welcome from the European Union and the United States - President Barack Obama hailed the election as a step toward restoring Ukrainian unity.
But although Putin told an international audience at the weekend he was ready to work with a new Ukrainian administration, Russia could still use the gaps in the election in the east to challenge its legitimacy.
A senior member of Putin's party, deputy parliamentary speaker Sergei Neverov, gave a taste of that when he wrote on Facebook: "It is hard to recognise the legitimacy of elections when tanks and artillery are wiping out civilians and a third of the population is driven to the polling stations at gunpoint."
In a statement, Obama did not pre-empt the results by naming Poroshenko but praised Ukrainians for turning out to vote. He called the election "another important step forward in the efforts of the Ukrainian government to unify the country and reach out to all of its citizens to ensure their concerns are addressed and aspirations met".