Russian President Vladimir Putin hosted the leaders of Armenia and Azerbaijan on Monday as he urged the arch-enemies to negotiate further steps in a peace agreement that ended weeks of deadly fighting over the Nagorno-Karabakh region.

The rare trilateral Kremlin talks with Armenian Prime Minister Nikol Pashinyan and Azerbaijan President Ilham Aliyev were the leaders' first post-war meeting to discuss the implementation of agreements signed last November to end six weeks of fighting over the ethnic Armenian enclave.

"Trilateral agreements are being progressively implemented,” Putin said.

"We are convinced that this creates necessary conditions for the long-term and full-fledged settlement of a decades-old conflict on the basis of justice, in the interests of both the Armenian and Azeri peoples.”

Putin thanked the two leaders for their cooperation with Russia’s mediation efforts aimed at "stopping the bloodshed, stabilising the situation and achieving a sustainable ceasefire”.

The Kremlin chief also said it was time to discuss "next steps” including the work of Russian peacekeepers stationed in Karabakh, demarcation lines and humanitarian issues.

Clashes over the disputed region of Nagorno-Karabakh broke out in late September last year, reigniting the conflict over the territory controlled by Armenia-backed separatists.

More than 6,000 people were killed in the war before the peace agreement that saw Armenia cede swathes of territory it had controlled for decades to its longstanding rival.

Moscow deployed nearly 2,000 peacekeeping troops to the region as part of the peace deal.

Nagorno-Karabakh proclaimed its independence from Baku following a war in the 1990s but its autonomy has not been recognised internationally, not even by Armenia.