In Moscow, Foreign Minister Sergey Lavrov said Russia appreciated Poroshenko's statements about the importance of Ukraine's ties with Russia and his pledge to negotiate an end to fighting in the east.
"We are ready for dialogue with representatives of Kiev, with Petro Poroshenko," Lavrov said at a briefing, adding it was a chance that "cannot be wasted." He emphasized that Moscow saw no need for any involvement by the United States or the European Union in those talks.
"We don't need any mediators," he said pointedly.
Lavrov also noted Russia's longstanding call for the Kiev government to end its military operation in eastern Ukraine.
Less than 20 percent of the polling stations in eastern Ukraine were open Sunday after gunmen intimidated residents by smashing ballot boxes, shutting down polling centers and issuing threats. But nationwide, about 60 percent of Ukraine's 35.5 million eligible voters turned out, and long lines snaked around polling stations in the pro-Western capital of Kiev.
Joao Soares, special coordinator for the OSCE observer mission in Kiev, hailed Sunday's vote even as he said monitors saw multiple threats, intimidation and abduction of election officials in the east.
"Ukrainian authorities should be commended for their efforts in the extraordinary circumstances to facilitate an election" which was held in parts of Ukraine's volatile east, Soares said.
With votes from 80 percent of the precincts counted Monday, Poroshenko was leading with about 54 percent of the vote in the field of 21 candidates. Former Prime Minister Yulia Tymoshenko was running a distant second with 13 percent. Election officials confirmed that Poroshenko had avoided a runoff.
Poroshenko struck a tone of unity Monday, saying he had no "rivals or political opponents in the race" and all of the other main candidates had congratulated him.
"More than ever, Ukraine now needs to be united," he said.
The election, which came three months after pro-Moscow President Viktor Yanukovych was chased from office following months of street protests, was seen as a critical step toward resolving Ukraine's protracted crisis.
Since Yanukovych fled in February, Russia has annexed Ukraine's southern Crimea Peninsula, the eastern regions of Luhansk and Donetsk have declared independence, and the interim Ukrainian government has launched an offensive to quash an uprising.
The interim Kiev government and the West have accused Russia of backing the separatist uprising. Moscow has denied the accusations.
President Barack Obama praised Ukrainians for participating in the voting "despite provocations and violence." He said the U.S. supports Ukraine's sovereignty and territorial integrity and is eager to work with the next president.
Vasilyeva reported from Kiev. Associated Press writers Vladimir Isachenkov and Lynn Berry in Moscow and Laura Mills in Kiev contributed to this report.