Russia has claimed it is ready to talk directly to Ukraine's new president, but warned the Kiev authorities not to intensify its armed operations against pro-Moscow separatists.
Foreign Minister Sergei Lavrov also said dialogue between Kiev and the eastern regions - where rebels have seized government buildings and fought troops - was the key to resolving the current crisis.
Billionaire Petro Poroshenko, who is on course to win Ukraine's presidential election, said he would not let insurgents turn the east into another Somalia.
The confectionery tycoon, nicknamed the "chocolate king", told reporters: "There are no talks with terrorists.
"Their goal is to turn Donbas (east Ukraine) into Somalia. I will not let anyone do this to our state and I hope that Russia will support my approach."
Mr Poroshenko has promised a dialogue with residents of eastern Ukraine and to guarantee their rights, including the right to speak Russian.
He said he was ready to work with those who have not taken up weapons, adding meetings with Russia should be held as soon as possible.
The 48-year-old self-made billionaire claimed he wanted to mend relations with Moscow but also supported strong ties with Europe.
However, in a reminder of the tough task ahead for the new leader, gunmen seized control of the airport in the main eastern city of Donetsk and forced it to close.
Mr Lavrov said Russia noted Mr Poroshenko's remarks about the importance of normalising ties with Moscow and the need to establish a dialogue with eastern regions.
He added that "we don't need any mediators", in a reference to a possible role of the United States and the European Union in such talks.
The election comes three months after pro-Moscow president Viktor Yanukovych was ousted by pro-Europe activists who were also protesting against corruption allegations.
In a statement, Mr Yanukovych said he respected the result of the poll.
He said: "It doesn't matter which region it was and what percentage of the population came to vote, whatever choice you made - I respect that choice, made in the most difficult time for our motherland."
Since Mr Yanukovych fled Kiev, Russia has annexed Crimea in southern Ukraine, and the eastern regions of Luhansk and Donetsk have declared their independence from Kiev.
The interim Ukrainian government also launched an assault in the east to quash an uprising that has left dozens dead.