Azerbaijan on Thursday said it had taken full control of its border with neighbouring Iran as Baku pressed its military operation in its conflict with Armenia over Nagorno-Karabakh.

The Nagorno-Karabakh region of Azerbaijan is controlled by Armenians, backed by Yerevan, who declared independence as the Soviet Union fell in a conflict that erupted again into full-scale fighting last month.

But Armenian forces have also been in control of seven surrounding districts of Azerbaijan, including a large swathe of the Azerbaijani border with Iran.

But President Ilham Aliyev said that with the capture of a settlement named Agbend, Baku now had full control of the border with Iran.

"The state border between Azerbaijan and the Islamic Republic of Iran has been completely secured through liberation of the Agbend settlement," he said on Twitter.

Azerbaijan has repeatedly boasted of military gains in the more than three weeks of fighting and on Wednesday Armenian Prime Minister Nikol Pashinyan acknowledged his country was facing "a difficult situation" on the frontline.

Baku has never hidden its desire to regain full control over Karabakh and the seven regions. But analysts say it will struggle to achieve this by military means alone.

Yet diplomacy also appears exhausted for now, with Pashinyan ruling out any diplomatic solution to the conflict for the moment and both sides further entrenching in their positions.

The foreign minsters of Azerbaijan and Armenia are to meet separately with US Secretary of State Mike Pompeo in Washington on Friday.

Yet hopes of a genuine ceasefire are fragile after two truces agreed over the last fortnight never showed any semblance of holding on the ground.

Meanwhile, the toll continues to mount.  

Yerevan says 874 Armenian soldiers and 36 civilians have been killed in the flare-up of fighting.

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

In an interview with AFP, the head of an International Committee of the Red Cross (ICRC) mission monitoring the conflict urged all parties to stop shelling civilians.

"We insist that the sides to the conflict comply with international humanitarian law," Gerardo Moloeznik said.