Russian Foreign Minister Sergey Lavrov on Monday said no changes were envisaged to the format for peace talks over Nagorno-Karabakh, after Azerbaijan proposed that its ally Turkey should be involved.
Mr Lavrov was in Moscow after talks with Armenian Foreign Minister Zohrab Mnatsakanyan.
Mr Mnatsakanyan said effective peace talks over Nagorno-Karabakh, a largely ethnic Armenian-populated enclave within Azerbaijan, would only be possible after a full ceasefire between Azeri and ethnic-Armenian forces.
Russia on Monday urged Armenia and Azerbaijan to immediately start observing a ceasefire agreed to over the breakaway Nagorno-Karabakh region as intense fighting between the two Caucasus rivals cast doubt over the accord.
After 11 hours of talks between the Armenian and Azerbaijani foreign ministers in Moscow, the two sides agreed on Saturday to a humanitarian truce.
But repeated clashes have made the truce deal seem shaky, with both sides on Monday accusing the other of repeated violations.
"We expect that the decisions that have been adopted will be rigorously observed by both parties," Mr Lavrov said.
He said the truce, the immediate aim of which was to exchange prisoners and bodies, had to be implemented and work was under way to ensure a means of verification was in place.
Mr Lavrov said he believed the "all-night vigil" that clinched the ceasefire would "not be in vain" and that the issue could be resolved soon.
Azeri and ethnic Armenian forces on Monday accused each other of launching attacks in and around Nagorno-Karabakh, in the heaviest fighting over the enclave for more than 25 years.
Analysts have long warned that Nagorno-Karabakh was the most combustible of the conflicts left over from the fall of the Soviet Union, with Azerbaijan vowing to regain control of the territory and Armenians insisting they would never cede ground.
Nagorno-Karabakh, which is populated and governed by ethnic Armenians, said its forces repelled Azeri army attacks overnight.
Armenian Defence Ministry spokeswoman Shushan Stepanyan said Azerbaijan was "intensively shelling the southern front".
Armenia said that "the adversary suffered great losses of manpower and military equipment" but provided no details.
The Azerbaijan Defence Ministry claimed: "Armenian armed forces, which did not comply with the humanitarian truce, repeatedly tried to attack the positions of the Azerbaijan army."
The ceasefire was already badly frayed on Sunday, when Azerbaijan said it launched air strikes against an Armenian regiment.
Armenia denied the claim.
The talks were the first diplomatic contact between the two former Soviet republics since fighting over the mountain enclave broke out on September 27.
About 500 people have been reported killed since.
The conflict has raised fears of a wider war drawing in Turkey, an ally of Azerbaijan, and Russia, which has a defence pact with Armenia.
Turkey has sent in Syrian mercenaries to fight alongside Azerbaijan, as it did for the Government of National Accord in Libya to widespread condemnation from the international community.
The renewed fighting is the worst since a 1994 ceasefire ended a war over Nagorno-Karabakh, which killed at least 30,000.
It has also raised concerns about the security of pipelines in Azerbaijan that carry Azeri natural gas and oil to Europe.