Ukraine's new leader, Petro Poroshenko, will take the oath in Kiev's parliament the day after he met with Russian President Vladimir Putin, widely seen in Ukraine as the country's nemesis, during World War II commemorations in northern France.
"The dialogue has begun, and that's a good thing," Poroshenko said on Ukrainian television after the brief encounter.
He added that a Russian representative would travel to Ukraine for talks on Sunday amid the first bilateral steps towards resolving their differences.
Putin and Poroshenko on Friday also jointly called for a ceasefire in the troubled southeast of Ukraine in a potential breakthrough in a crisis that has poisoned Moscow's relations with the West.
Poroshenko, a 48-year-old billionaire, was elected with 54.7 percent of the votes in presidential elections on May 25.
His inauguration ceremony will be attended by a range of foreign VIPs, including US vice president Joseph Biden and European council President Herman Van Rompuy.
Poroshenko will assume the presidency as the formal successor of Viktor Yanukovych, who was ousted in February after bloody street fighting in downtown Kiev and who is now living in exile in Russia.
Heavy task ahead
Ahead for Poroshenko lies the tough task of bringing his country closer to Europe, a crucial issue for many who took part in the movement that brought down the previous administration.
He must also try to end the recession that has plagued the country for the past two years, but above all he must unite his country even as it teeters on the brink of civil war.
A step in that direction may have been taken in France, when he shook hands with Putin.
The meeting, on the sidelines of the events in Normandy to mark the 70th anniversary of the D-Day landings, was the first between the two men since Poroshenko won Ukraine's presidential election.
Moscow had previously said it was ready to work with the new president but stopped short of explicitly recognising him as the legitimate leader of the Ukrainian people.
US President Barack Obama, who also met with Putin in France on Friday, told NBC Nightly News that Russia has to recognise Poroshenko as legitimate if it wants to resolve months of crisis.
"Mr. Putin should be working directly with Mr. Poroshenko and the government of Ukraine to try to resolve differences between the two countries," Obama said.
Russia also needs "to stop financing and arming separatists who have been wreaking havoc in the eastern part of the country," Obama added.
Tensions in southeastern Ukraine have mounted in recent days with the government admitting on Thursday that it had lost control of three border posts that were being routinely attacked by the rebels.
On Friday, insurgents shot down a Ukrainian military cargo plane near Slavyansk, a hotbed of rebel activity. The crew reportedly managed to eject before impact.
Also near Slavyansk on Friday, one police officer was killed and two others injured in a mortar attack.
Truce talks in coming days
A French official said Friday's Putin-Poroshenko meeting had lasted around 15 minutes.
"They were able to begin a dialogue on possible de-escalation measures including Moscow recognising Poroshenko's election," he added.
"The practicalities of a ceasefire will also be discussed in the coming days."
The Kremlin has indicated that it will be sending an ambassador to Kiev for Poroshenko's investiture on Saturday in a move some have interpreted as de facto recognition of the new president's legitimacy.
A ceasefire could be harder to deliver. For it to be acceptable to the pro-Moscow rebels, there would have to be some sort of pullback by Ukrainian government forces, which Kiev would regard as an infringement of its right to police all of its sovereign territory as it sees fit.
The Russian president has repeatedly emphasised that he does not control the Ukraine rebels while Western powers accuse Moscow of pulling the strings.
According to French Foreign Minister Laurent Fabius, Putin admitted he could have a "certain influence but not total influence" over events in Ukraine.
In their meeting on Friday, the two leaders also discussed some of the economic aspects of the crisis, the most important of which is Russian energy giant Gazprom's doubling of the price of gas it supplies to Ukraine and its demands for a rapid settlement of the country's arrears.
The meeting followed Putin's talks with British Prime Minister David Cameron in Paris on Thursday. Those two encounters were the Russian leader's first since Russia's annexation of the Crimean peninsula, previously part of Ukraine, in March.