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A Kremlin spokesman confirmed the news, Russian agencies reported on Tuesday. There was no official immediate reaction from Baku.
Arayik Harutyunyan, the leader of the Nagorno-Karabakh region, said on Facebook that he gave agreement "to end the war as soon as possible".
The declaration has followed six weeks of heavy fighting and advancement by the Azerbaijan's forces. Baku said on Monday it had seized dozens more settlements in Nagorno-Karabakh, a day after proclaiming victory in the battle for the enclave's strategically positioned second-largest city.
"The decision is made basing on the deep analyses of the combat situation and in discussion with best experts of the field," Pashinyan said on social media.
"This is not a victory but there is not defeat until you consider yourself defeated. We will never consider ourselves defeated and this shall become a new start of an era of our national unity and rebirth."
The fighting had raised fears of a wider regional war, with Turkey supporting its ally Azerbaijan, while Russia has a defence pact with Armenia and a military base there.
Azerbaijan says it has since September 27 retaken much of the land in and around Nagorno-Karabakh that it lost in a 1991-94 war which killed an estimated 30,000 people and forced many more from their homes. Armenia has denied the extent of Azerbaijan's territorial gains.