The foreign ministers of Armenia and Azerbaijan will meet separately this week with US Secretary of State Mike Pompeo as world powers seek to halt the fighting over Nagorno-Karabakh.

Azerbaijan Foreign Minister Jeyhun Bayramov and Armenian counterpart, Zohrab Mnatsakanyan will both meet Mr Pompeo in Washington on Friday, the two foreign ministries said.

However they both ruled out a possibility of a trilateral meeting.

World powers including Russia and the United States have expressed dismay that there has been no let-up in more than three weeks of fighting over Nagorno-Karabakh.

A truce was agreed earlier this month in Moscow and another this weekend but the accords have had next to no impact on the ground.

Yerevan says 772 Armenian soldiers and 36 civilians have been killed in the current flare-up of fighting. 

Baku reported 63 civilian casualties and has yet to disclose its military losses.

Azerbaijan and the Armenian separatists who control its Karabakh region have been locked in a bitter impasse over the fate of the mountainous province since a war in the 1990s that left 30,000 people dead.

Their long-simmering conflict erupted again on September 27 in fierce clashes that raised alarm over the failure of decades-long international mediation.

Along with France and Russia, the United States co-chairs the so-called Minsk Group of international mediators to the Karabakh peace talks since the 1994 ceasefire.

Azerbaijan has repeatedly claimed military success in the current fighting by taking control of areas both within Karabakh and other Azerbaijani territory that had been held by Armenian forces.

In an address to the nation, Azerbaijani President Ilham Aliyev said the army had taken control of some 20 more villages in Azerbaijan's Armenian-held districts surrounding Karabakh. 

"I am once again urging Armenian leaders: leave Azerbaijani territories before it's too late and we will then cease fire," he said.

However Armenian Prime Minister Nikol Pashinyan urged international recognition of Karabakh, claiming on Twitter that making Armenians there "live under Azerbaijani rule violates international law".

Analysts say Azerbaijan is unlikely to be able to retake control of Karabakh through military means alone, while the seemingly irreconcilable positions on both sides makes a diplomatic solution elusive.