The foreign ministers of Armenia and Azerbaijan on Saturday held their first one-on-one talks since the 2020 war between the arch-foes for control of the disputed Nagorno-Karabakh region, officials said.

Held in the Georgian capital Tbilisi, the talks were expected to build on an agreement the Caucasus countries' leaders reached under EU mediation in May to "advance discussions" on a future peace treaty.

Armenian Foreign Minister Ararat Mirzoyan and his Azerbaijani counterpart Jeyhun Bayramov "discussed a wide range of issues related to normalising relations between the two countries," the Armenian foreign ministry said in a statement.

Mirzoyan "stressed the importance of the Karabakh conflict's political resolution for building a lasting peace in the (Caucasus) region" and called on Baku to release Armenian POWs, the ministry said.

The Azerbaijani foreign ministry said Bayramov demanded "the withdrawal of the Armenian armed forces from the territory of Azerbaijan," referring to the parts of Karabakh still under Armenian separatists' control.

He also "noted the importance of clarifying the fates of nearly 4,000 missing Azerbaijanis," the foreign ministry in Baku said.

"The ministers pledged to continue the direct dialogue between Azerbaijan and Armenia."

The atmosphere was tense ahead of the meeting as both countries' defence ministries traded accusations of initiating an overnight shootout at their shared border.

Armenia and Azerbaijan fought two wars -- in 2020 and in the 1990s -- over Azerbaijan's Armenian-populated region of Nagorno-Karabakh.

Six weeks of fighting in autumn 2020 claimed more than 6,500 lives and ended with a Russian-brokered ceasefire agreement.

Under the deal, Armenia ceded swathes of territory it had controlled for decades, and Russia deployed some 2,000 peacekeepers to oversee the fragile truce.

Following its invasion of Ukraine on February 24, increasingly isolated Moscow lost its status as a primary mediator in the conflict.

The European Union has since led the Armenia-Azerbaijan normalisation process, which involves peace talks, border delimitation and the reopening of transport links.

Aliyev and Armenian Prime Minister Nikol Pashinyan met in Brussels in April and May and European Council President Charles Michel has said their next meeting is scheduled for July or August.

Ethnic Armenian separatists in Nagorno-Karabakh broke away from Azerbaijan when the Soviet Union collapsed in 1991. The ensuing conflict claimed around 30,000 lives.