Russian President Vladimir Putin and his Ukrainian counterpart Volodymyr Zelensky agreed on a full and comprehensive implementation of a cease-fire in eastern Ukraine before the end of 2019 during their first face-to-face meeting on Monday.

The two leaders, meeting in Paris, also agreed to exchange all remaining prisoners captured in the conflict zone in Ukraine's east by the end of this month after the nine-hour talks, which had been brokered by French President Emmanuel Macron and German Chancellor Angela Merkel.

The negotiations took place under the diplomatic framework of the so-called Normandy Quartet, which draws in France and Germany as countries assisting in efforts to bring peace to eastern Ukraine.

Following the talks, the four leaders also agreed to give their support to the implementation of an updated plan for demining operations in the conflict zone, and for an agreement within the Trilateral Contact Group, or TCG, on three additional disengagement zones. This would see the disengagement of forces and equipment in the contested areas by the end of March 2020, a joint declaration by the leaders said.

The TCG comprises representatives from Ukraine, Russia and the Organization for Security and Cooperation in Europe. It aims to facilitate a diplomatic resolution to the fighting in Ukraine's eastern Donbass region, where conflicts between government troops and pro-independence militias have been raging since April 2014.

In the joint declaration, the four leaders called on the TCG to facilitate an "all for all" prisoner swap by the end of the year.

Monday's meeting was the first of its kind since leaders met in Berlin in 2016. With Zelensky having taken office earlier this year, it provided the first opportunity for him to meet Putin.

The four leaders hailed the meeting as marking progress in reviving a peace process that had been laid down in the Minsk Accords. Those agreements, which were signed in September 2014 and February 2015, are aimed at bringing the conflict in Donbass to a peaceful end.

Prisoner exchanges

Specifically, the agreements envisage a cease-fire, a withdrawal of heavy weaponry from the demarcation line, prisoner exchanges and local elections, among other measures.

Macron, as the host of the landmark event, said the talks were "rich and fruitful", adding that "we have made progress on disengagement, prisoner exchanges, ceasefire and a political evolution".

"We have asked our ministers in the coming four months to work on this," he said.

Merkel said "it is very important to ensure an immediate cease-fire", adding that the implementation of local elections "is not easily achievable" and much more work needs to be done.

Putin said that the four leaders welcomed the disengagement of forces in Donbass.

"Every step on the way toward de-escalating the situation in southeastern Ukraine is important, along with ensuring a comprehensive cease-fire. We hope that the disengagement of forces will continue step by step," he said.

According to the Xinhua News Agency, Putin and Zelensky had a separate meeting after the four-party talks.

Zelensky said the talk with Putin was "positive", and that there will be a new round of prisoner swaps this month.

However, Zelensky said there were still gaps between the positions of Ukraine and Russia.

Zelensky, who was elected on a promise to resolve the conflict, felt pressures from public opinion at home, said Reuters, which cited the concerns held by many Ukrainians over the consequences of compromise with Russia.

Protesters were camped outside the presidential administration compound in the Ukrainian capital Kiev, where they watched news footage of the leaders' meeting on a big screen.

"I would like to solve more problems," said Zelensky, stressing that the proposed local elections must be held in accordance with Ukrainian laws.

Zelensky said he had given no ground on Ukraine's sovereignty or territorial integrity, adding that he and Putin had disagreed on several issues.

The Ukrainian president had to contend with blunt questions from Russian journalists at the news conference after the meeting. When asked who had triumphed in their exchanges, Zelensky responded: "I don't know who (beat) whom. I think it would be appropriate to be diplomatic as we've just started talking. Let's say for now it's a draw."