The American, Russian and incoming Ukrainian leaders have discussed, in separate meetings in France, a ceasefire and other possible steps to de-escalate the ongoing crisis in Ukraine, reports said.
Russian President Vladimir Putin held brief one-on-one talks on Friday with his US counterpart Barack Obama and Ukraine's Petro Poroshenko, in a possible diplomatic breakthrough that played out amid continuing violence in eastern Ukraine.
In remarks to reporters, Putin said the meetings with Poroshenko and other Western leaders were positive, and described talks with Obama as "substantial".
"I think the exchange of views was very positive," he said after attending the ceremonies marking the 70th anniversary of D-Day alongside US, British, French and German leaders.
Putin, however, said that Poroshenko, who will take his oath as president of Ukraine on Saturday, must first stop "punitive" operations in the eastern part of his country.
"Ukraine must demonstrate its good will. The repressive operation must be stopped."
It was the first meeting between the two men since pro-Western chocolate tycoon Poroshenko won Ukraine's presidential election on May 25.
Poroshenko welcomed the start of a dialogue with Putin and said it has "a good chance" of succeeding.
"The dialogue has begun, and that's a good thing," he said on Ukrainian television.
"A Russian representative will travel to Ukraine, and we will discuss with him the first steps towards a plan [to resolve] the situation... We have a good chance of implementing it."
The talks will take place on Sunday, he said.
Meanwhile, US Deputy National Security Advisor Ben Rhodes told the AFP news agency that during their separate meeting, Obama told Putin he must de-escalate tensions in Ukraine, or face deeper international isolation.
Russia's annexation of Crimea in March and the continuing standoff between pro-Russian fighters and the Ukrainian army the country's east have plunged Moscow's relations with the US and the European Union to a post-Cold War low.
Hollande's office have been planning for weeks to use the World War II anniversary celebration to try to break the ice in the crisis.
World leaders and veterans earlier on Friday paid tribute to soldiers who fell in the liberation of Europe from Nazi German rule, at a series of ceremonies around the Normandy beaches where allied forces landed on June 6, 1944.
Our victory in that war decided not just a century, but shaped the security and well-being of all posterity.
Wreaths, parades and parachute-drops honoured history's largest amphibious assault, in which 160,000 US, British and Canadian troops waded ashore to confront German forces, hastening its defeat and the advent of peace in Europe.
Flanked by war veterans, Obama joined Hollande to commemorate the victory and reaffirm US-French solidarity before the marble headstones of fallen US soldiers at the Normandy American Cemetery.
"Our victory in that war decided not just a century, but shaped the security and well-being of all posterity," Obama said.
He sought to link the sacrifices of World War II to US servicemen killed in combat since the September 11, 2001 attacks on the US by al-Qaeda.
Twenty-one foreign leaders attended the commemorations, including Britain's Queen Elizabeth .
More fighting in Ukraine
Meanwhile in Ukraine, Al Jazeera's David Chater reported that a government supply plane was shot down by pro-Russian rebels in Slovyansk.
A Ukrainian police officer was also killed, and two others were injured in Slovyansk after pro-Russian rebels launched a mortar attack on a checkpoint, Deputy Interior Minister Serhiy Yarovy said.
Earlier on Friday, Anton Herashchenko, an aide to Ukraine's interior minister, said government troops have killed a group of armed men, who came from Russia in trucks and an infantry vehicle, and tried to cross the border at the village of Marynivka late on Thursday.
Herashenko said the attackers were supported by about 100 rebels who came from the Ukrainian side of the border.
Al Jazeera's Kim Vinnell, reporting from the town of Marynivka, also quoted Ukrainian military sources as saying that soldiers were wounded in the attack.
Government troops have for weeks been clashing with pro-Russian rebels who dismiss the Kiev government as illegitimate.
On Thursday, the Group of Seven industrial nations warned of tougher sanctions against Russia , if it continues to arm separatist rebels in Ukraine.