Moscow and Kiev promised to resume dialogue on Monday after preliminary results suggested that the pro-west businessman Petro Poroshenko had won Ukraine's presidential election – although renewed fighting in the east of the country dampened hopes of an immediate solution to the crisis.

Russia's foreign minister, Sergei Lavrov, said Moscow was ready to enter talks with the new leadership, in his country's first high-level response to Saturday's election. "We shouldn't miss the chance that we have now to establish an equal dialogue of mutual respect considering the vote that has taken place, the results of which Russia is ready to respect," Lavrov said.

Pro-Russia forces who have occupied government buildings in eastern Ukraine since April followed Moscow's lead in welcoming Poroshenko's election. Denis Pushilin, supreme council chairman of the self-declared Donetsk People's Republic, said they were ready to negotiate with Ukraine's new leadership, but only with the participation of intermediaries including Russia.

Violence flared in the east on Monday morning when armed men seized Donetsk airport. There were reports of gunfire later in the day.

Late on Sunday night the first deputy PM, Vitaly Yarema, promised that Kiev's "anti-terrorist operation" would be renewed after a pause during the presidential vote, which in the Donetsk and Luhansk regions involved only a handful of polling stations.

Lavrov said the renewal of the anti-terrorist operation would be a "colossal mistake" and could threaten the resumption of dialogue.

Poroshenko has not backed off from the harsh tone struck by Kiev regarding the armed rebels in the two regions, repeating on Monday that there could be no negotiations with terrorists and comparing the pro-Russian militia men to Somalian pirates.

But he said he would try to gain the trust of residents in the east, who have looked at the Kiev government with extreme suspicion. He has promised that his first trip as president will be to eastern Ukraine.

"We will try to win the trust of those who didn't vote for me," Poroshenko told journalists. "Now the main mission is the unification of the state, the establishment of peace and the eradication of lawlessness."

He also promised to return Crimea to Ukraine, arguing that the annexation of the territory was hurting Russia's economy. A key point in any negotiations with Moscow will be the price at which Ukraine purchases Russian natural gas. Moscow has demanded Ukraine pay back billions of dollars it saved on a significantly reduced gas price under the former president Viktor Yanukovich.

Poroshenko called for negotiations with Moscow in the presence of international intermediaries. Lavrov said Russia was ready to work with the US and the EU on realising the OSCE-drafted roadmap to defuse the crisis. But he said Russia did not need an intermediary in its bilateral relations with Ukraine, especially not the former Georgian president Mikheil Saakashvili, as suggested by Poroshenko's ally Vitali Klitschko, the newly elected mayor of Kiev.