MOSCOW — Azerbaijan and Armenia exchanged prisoners Monday, a move stipulated in the peace deal between the two ex-Soviet nations that ended recent fighting over the separatist territory of Nagorno-Karabakh.

Azerbaijani authorities said an all-for-all exchange of prisoners and hostages have been agreed with Armenia, and a plane with some of the captives landed in Azerbaijan on Monday afternoon.

On Monday evening, Deputy Prime Minister of Armenia Tigran Avinyan announced that 44 captives have also returned to Armenia from Azerbaijan.

“At this stage, the Armenian captives whose captivity has been confirmed by Azerbaijan and the Red Cross are being returned. The process of finding and organizing the return of our other compatriots who are missing and have been possibly captured continues,” Avinyan wrote on his Facebook page.

The exchange was facilitated by Russian peacekeepers that have been deployed to Nagorno-Karabakh under the peace deal. Russia’s Defense Ministry said Monday that 12 captives were handed over to Azerbaijan and 44 to Armenia.

It wasn’t immediately clear how many more prisoners the two countries intend to exchange.

Nagorno-Karabakh lies within Azerbaijan but has been under the control of ethnic Armenian forces backed by Armenia since a separatist war there ended in 1994. That war left not only Nagorno-Karabakh but substantial territories around it in Armenian hands.

Heavy fighting erupted in late September and marked the biggest escalation of a decades-old conflict between Armenia and Azerbaijan, killing more than 5,600 people on both sides.

A Russian-brokered peace agreement that took effect Nov. 10 halted the violence and stipulated that Armenia hand over control to Azerbaijan of some areas it holds outside Nagorno-Karabakh’s borders. Azerbaijan also retained control over areas of Nagorno-Karabakh it has taken during the conflict, and both sides agreed to exchange prisoners, hostages and bodies of the victims of the fighting.

In accordance with the agreement, nearly 2,000 Russian peacekeepers have been deployed to Nagorno-Karabakh under a five-year mandate.

The peace deal was celebrated in Azerbaijan as a major triumph, and last week a massive military parade was held in Baku to mark it. In Armenia, the truce sparked outrage and mass protests, with thousands regularly taking to the streets to demand the ouster of the country’s prime minister over his handling of the conflict.

Armenian Prime Minister Nikol Pashinyan has defended the deal as a painful but necessary move that prevented Azerbaijan from overrunning the entire Nagorno-Karabakh region. On Monday, Pashinyan announced three days of mourning to start on Saturday to honor the victims of the fighting.

Thousands of people rallied in the Armenian capital, Yerevan, once again on Monday, chanting “Nikol, go away!” and “Armenia without Nikol!”