Armenia and Azerbaijan on Monday mourned thousands of people killed in their brief but brutal war for control of the Nagorno-Karabakh region on the first anniversary of the conflict.

People in both countries observed a minute of silence and congregated for memorial services in churches and mosques in memory of those left dead in six weeks of fighting that erupted on September 27 last year.

The war for control of the mountainous region left some 6,500 people dead and sparked mutual allegations of war crimes.

It ended in November with a Russian-brokered ceasefire that saw Armenia hand over to Baku swathes of contested territories it had controlled for decades.

"We will forever keep our martyrs in our hearts," Azerbaijani President Ilham Aliyev said in a televised address to the nation.

"If we see that there is a new threat facing our people or state, we will crush Armenian fascism again," he said.

At noon local time, traffic halted across Azerbaijan and passersby stood for a minute of silence nationwide.

Thousands of troops marched in downtown Baku holding photos of the soldiers killed in action.

Armenian Prime Minister Nikol Pashinyan laid a wreath at the Eralbur military cemetery in Yerevan on Monday morning, before visiting a medical centre for war veterans.

"I bow before the memory of the dead and before their families," Armenia's President Armen Sarkisian wrote on Facebook.

On Sunday evening, around 3,000 Armenians staged a torch-lit march from the centre of capital Yerevan towards a memorial cemetery to commemorate the war victims.

Ethnic Armenian separatists in Nagorno-Karabakh broke away from Azerbaijan as the Soviet Union collapsed, and an ensuing conflict claimed around 30,000 lives.

At the time, Armenians took control of the enclave as well as seven nearby districts of Azerbaijan -- some 20 percent of the country's national territory.

The fresh war last year saw Baku recapture parts of Karabakh and all of the surrounding districts.

Moscow has deployed some 2,000 peacekeepers in the area to oversee the ceasefire.

Both countries filed applications in the International Court of Justice, accusing each other of war crimes.