Plans for US Secretary of State Mike Pompeo to meet the foreign ministers of Azerbaijan and Armenia on Friday raised hopes this week that the two former Soviet republics would agree to end their deadliest fighting since the mid-1990s.

But those hopes have been dented by the continued heavy fighting in and around Nagorno-Karabakh, a breakaway territory which is inside Azerbaijan but controlled by ethnic Armenians, and by angry rhetoric from both sides.

Armenia's prime minister said on Wednesday he could see no diplomatic resolution of the long-running conflict at this stage. Azerbaijan's president said on Tuesday his country would reclaim Nagorno-Karabakh by force.

Hundreds of people have been killed since fighting flared on September 27, raising fears of a wider war drawing in Turkey and Russia and increasing concerns about the security of pipelines in Azerbaijan that carry Azeri gas and oil through the South Caucasus to world markets.

Russia has brokered two ceasefires since September 27 but neither has held.

Azerbaijan's defence ministry reported fighting in several areas on Thursday, including territories close to the line of contact that divides the sides.

It also said Armenia had fired three ballistic missiles at three regions inside Azerbaijan but Armenia said this was "complete nonsense and a cynical lie."

The Armenian defence ministry reported fighting in several areas, and Nagorno-Karabakh officials said the town of Martuni and nearby villages in the enclave had been shelled.

Azerbaijan wants to regain control of Nagorno-Karabakh before it agrees to end fighting. Armenia says it will not allow this and accuses Azerbaijan of making a land grab in the recent fighting.

Azeri President Ilham Aliyev said this month he believed there was a military solution to the conflict and his aide Hikmet Hajiyev said on Wednesday Azerbaijan did not expect any breakthrough at the talks in Washington.

Azeri forces, bolstered in recent years by increased military spending and the purchase of weapons from Turkey, say they have made territorial gains in the latest fighting though Nagorno-Karabakh says its forces have repulsed repeated attacks.

Armenian Prime Minister Nikol Pashinyan underlined how far apart the sides are on Wednesday, saying: "Everything that is diplomatically acceptable to the Armenian side ... is not acceptable to Azerbaijan any more."

Pashinyan had previously said that Armenia was ready for talks based on mutual concessions and a solution acceptable to all sides of the conflict.

Pompeo said on Wednesday he still hoped a diplomatic solution could be found and underlined that the "right path forward is to cease the conflict, tell them to de-escalate, that every country should stay out."

Turkey has said it will not hesitate to send soldiers and provide military support for Azerbaijan if such a request is made by its close ally. Russia has a defence pact with Armenia but Pashinyan has said he does not advocate Russian military involvement in the conflict.

Australian Associated Press