Russian President Vladimir Putin has said he hopes the U.S. can help Moscow broker a solution to end the conflicts in the region of Nagorno-Karabakh.

Putin's remarks came ahead of foreign ministers of Azerbaijan and Armenia to meet U.S. Secretary of State Mike Pompeo this week in Washington, as new ground fighting incidents are reported to continue in the region.

"I very much hope that our American partners will act in unison with us and will help the settlement," Putin told a meeting of the Valdai Discussion Club on Thursday. Putin added that he was in "constant" communication with leaders of Armenia and Azerbaijan where he talks to them on the phone "several times a day," but those hopes were dented by the continued heavy fighting in and around Nagorno-Karabakh.

Putin said Moscow believed that nearly 5,000 people had been killed in fighting between Azerbaijan and ethnic Armenian forces, with more than 2,000 dead on each side.

On the battlefield, the Nagorno-Karabakh authorities said 874 of its military personnel had been killed since September 27, in addition to 37 civilians. While Azerbaijan told 63 Azeri civilians had been killed and 293 wounded. So far Azerbaijan has not disclosed its military casualties.

The Armenian side reported fighting in several areas on Thursday, and Nagorno-Karabakh's local officials said the town of Martuni and nearby villages in the enclave had been shelled. Azerbaijan also reported fighting in several areas, including territories near the line of contact that divides the two sides. It also said Armenia had fired three ballistic missiles at three regions inside Azerbaijan, which was denied by Armenia.

With military support from Turkey, Azeri forces say they have made territorial gains in the latest fighting, including full control over the border with Iran.

In an exclusive interview with Nikkei on Wednesday, Azerbaijan President Ilham Aliyev said he is open to a trilateral meeting with the Armenian prime minister in Moscow, but claimed that "counterproductive and provocative statements" by the Armenians render "negotiations senseless."

Aliyev said his country is always the strongest supporter of Turkish active involvement in the Caucasus region, and for Azerbaijan Turkey is a brotherly country and the closest ally. He reaffirmed Azerbaijan's support for Turkey to become a co-chair of the Minsk group.

President Putin has said Russia disagreed with Turkey on the Nagorno-Karabakh issues, but both countries needed to find a compromise. Turkish President Tayyip Erdogan "might seem tough, but is a flexible politician and reliable partner for Russia," Putin said.

NATO chief Jens Stoltenberg has said on Thursday both Armenia and Azerbaijan were valued partners of the alliance and refused to take sides in the fighting. He did suggest that Turkey must be part of a diplomatic solution to the conflict, and deplored reports of civilian deaths.

One day before, Stoltenberg had met Armenia's President Armen Sarkisian at NATO's Brussels headquarters.

(With input from agencies)