Poroshenko, known for his pragmatism, supports building strong ties with Europe but also has stressed the importance of mending relations with Moscow. Upon claiming victory, he said his first step as president would be to visit the east.
He said he hoped Russia would support his efforts to bring stability and that he wanted to hold talks with Moscow.
Russia denies allegations that it supports or directs the insurgents. But Russia is pushing for Ukraine to decentralize its government, which would give more power to the regions including the east, and wants Kiev to withdraw its troops from the area. Russia massed its troops near the Ukrainian border, but President Vladimir Putin said last week that those forces were being pulled back to their home bases.
After Russia annexed the southern region of Crimea from Ukraine in March, many Ukrainians feared Moscow wanted to invade the east.
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 the fighting.
"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 U.S. or the European Union in those talks.
"We don't need any mediators," he said pointedly.
The rebels had vowed to block the election in the Donetsk and Luhansk regions, and more than 80 percent of the polling stations were closed there after gunmen intimidated residents by smashing ballot boxes, shutting down voting centers and issuing threats.
But nationwide, about 60 percent of Ukraine's 35.5 million eligible voters turned out, and long lines were reported at polling stations in the capital.
Joao Soares, special coordinator for the OSCE observer mission in Kiev, hailed the vote and the "clear resolve of the authorities, which resulted in a genuine election largely in line with international commitments."
"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.
He said monitors saw multiple threats, intimidation and abduction of election officials in the east.
With votes from 75 percent of the precincts counted, Poroshenko was leading with about 54 percent in the field of 21 candidates. Former Prime Minister Yulia Tymoshenko was running a distant second with 13 percent. If those results hold, Poroshenko would avoid a runoff election next month. Authorities said official results would be announced by June 5.
Vasilyeva reported from Kiev. Associated Press writers Jim Heintz, Vladimir Isachenkov and Lynn Berry in Moscow and Laura Mills in Kiev and Alexander Zemlianichenko in Slovyansk contributed to this report.