It comes a week after a Russia-brokered truce frayed immediately after it took force.
The two sides traded blame for breaching that deal.
The new agreement was announced by the Armenian and Azerbaijani foreign ministers following phone calls between Russian foreign minister Sergey Lavrov and his counterparts.
Mr Lavrov strongly urged the countries to abide by the Moscow deal.
Nagorno-Karabakh lies within Azerbaijan but has been under the control of ethnic Armenian forces backed by Armenia since a war there ended in 1994.
The latest fighting that began on September 27 has involved heavy artillery, rockets and drones, killing hundreds in the largest escalation of hostilities between the South Caucasus neighbours in more than a quarter-century.
The reported death toll in clashes over the separatist territory has reached around 600.
Nagorno-Karabakh military officials said 16 more of their servicemen had been killed in fighting on Tuesday, bringing total number of dead among military members to 532 since September 27, when the fighting started.
Azerbaijan has not disclosed its military losses, and the overall toll is likely to be much higher with both sides regularly claiming to have inflicted significant military casualties on one another.
Azerbaijani authorities said 42 civilians have been killed on their side in over two weeks. Nagorno-Karabakh human rights ombudsman Artak Beglaryan reported at least 31 civilian deaths in the breakaway region late on Monday. Hundreds more have been wounded.
Both sides have repeatedly accused each other of attacks amid appeals from around the globe to end the hostilities and start peace talks.
Armenian and Azerbaijani foreign ministers signed a ceasefire deal last week.
The truce that took effect on Saturday was brokered by Russia, which has a security pact with Armenia.
But Moscow has also cultivated warm ties with Azerbaijan and seeks to mediate in the conflict.
The truce, however, has been immediately challenged with both Armenia and Azerbaijan accusing each other of continued attacks in violation of the agreement.
On Tuesday, Azerbaijani officials have once again accused Armenian forces of shelling some of its regions, and Nagorno-Karabakh officials said Azerbaijan launched “large-scale military operations” along the front line.
Russia and the European Union had urged both sides to observe the ceasefire.
