A thousand people took to the streets of the Armenian capital Yerevan on Sunday demanding the authorities take action to find soldiers missing in recent fighting with Azerbaijan over Nagorno-Karabakh.

The protesters, including several local celebrities, marched through Yerevan holding up photos of the missing soldiers and posters that read "Help return our captives".

At the start of the march, the demonstrators read out a letter addressed to the Russian ambassador in Yerevan asking him to "personally intervene in the process" and pass on their request to Moscow.

The six weeks of fighting over the restive region were halted by a Russia-brokered peace deal that was signed by the ex-Soviet rivals on November 9.

Under the document, Azerbaijan reclaimed swathes of territories that for three decades were held by Armenian separatists.

The accord also provided for the exchange of prisoners and bodies.

AFP journalists reported that a smaller gathering of 30 people took place on Saturday in Karabakh's main city Stepanakert.

Demonstrators briefly blocked a main street in the city until their representatives were received by Arayik Harutyunyan, the president of the self-proclaimed republic.

"We are calling for immediate action to resolve the problem. But the authorities say that it is not up to them, that it depends on the Azerbaijanis," 47-year-old Arsen Ghukasyan said after the meeting.

Ghukasyan says he is searching for his son and brother who was last in touch in early October, less than a week after fresh clashes broke out over Nagorno-Karabakh, an ethnic Armenian enclave that declared independence from Baku during a war in the 1990s.

Another man, who is looking for his son, said the missing soldiers are "waiting for the Armenians to come and rescue them".

"But we, parents, are without hope. We do not know how to save our children," the 47-year-old father added.

Karabakh rights ombudsman Artak Beglaryan said on Friday that around 50-60 Armenian soldiers were being held as prisoners in Azerbaijan.

Armenian authorities have reported more than 2,300 military casualties while Baku has not disclosed army losses.

The International Committee of the Red Cross has overseen the exchange of casualties under the protection of Russian peacekeepers who have been deployed to the region.

"The enemy could have identified martyr Fakhrizadeh either through intelligence work or direct interviews,” he added.

Firebrand MP Javad Karimi Ghodousi, had on Friday accused Rouhani of setting up a meeting between Fakhrizadeh and IAEA officials in the past — a claim strongly denied by the Rouhani administration.