Russia's foreign minister has said the Kremlin is "ready for pragmatic dialogue" with Petro Poroshenko, Ukraine's would-be president, without any Western mediation.
Sergey Lavrov's comments on Monday came as Poroshenko - leading with about 54 percent in Ukraine's presidential elections according to figures from 75 percent of the precincts - said he hoped to meet Russia's leaders in the first half of June.
Lavrov said Russia had noted Poroshenko's statements about the importance of normalising ties with Moscow and the need to establish a dialogue with pro-Russian separatists in the country's east.
"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," he said.
"As the president [Vladimir Putin] has said, we respect the result of the choice of the Ukrainian people."
However, Lavrov cautioned Ukraine against resumption of military crackdown, dubbed "anti-terrorist operations" by Kiev, on the rebels.
"Perhaps the most important thing is that the current government respect its citizens, have respect for the people and achieve compromise agreements that take into account the interests of all forces, all ethnic and religious groups, because without this hardly anything can happen," he said.
Poroshenko has said he wants to continue the military offensive, but also to make it more "efficient".
"I hope Russia will support efforts to tackle the situation in the east [of Ukraine]," he said, adding that he would also use all legal means to secure the return of Crimea region to Ukraine, annexed by Russia in March.
For his part, Viktor Yanukovich, Ukraine's ousted president, said on Monday he respected the result of the presidential polls, but he cast doubt on the vote's legitimacy.
"For the legitimacy of the election and the legitimacy of the president himself, the participation of the south and east of our country is necessary," he said.
Armed pro-Russian separatists have taken control of some towns and cities in mainly Russian-speaking eastern Ukraine and they prevented many people in the region from taking part in Sunday's presidential election.
Yanukovich condemned authorities in Kiev who took control after his overthrow in February, saying that "many voters in these regions were insulted and humiliated by the actions of the illegitimate authorities who came to power as the result of an armed coup."
Later on Monday, armed pro-Russian separatists took over Donetsk's international airport terminal in eastern Ukraine on Monday after forcing its closure to flight. Reuters news agency reporter later heard gunfire and explosions in the vicinity.