US Secretary of State Antony Blinken welcomed the steps Armenia and Azerbaijan were taking to achieve peace after recent deadly clashes between them, State Department spokesman Ned Price said.
Mr Blinken told Armenia's Ararat Mirzoyan and Azerbaijan's Jeyhun Bayramov that diplomacy was the only way to achieve sustainable peace, Mr Price said.
The meeting between the three diplomats came a week after Armenia and Azerbaijan accused each other of breaching a ceasefire agreement that ended days of deadly clashes.
At least 286 people were killed in the violence between the neighbouring countries last month before a US-brokered truce halted the violence.
“In a week that has been marked by too much violence, including the deaths of Armenian soldiers and Azerbaijani civilians in landmine explosions, he welcomed the meeting between the ministers on October 2 as an important step forward in the peace process,” Mr Price said.
Mr Mirzoyan and Mr Bayramov met in Geneva on Sunday to begin “drafting the text of the peace treaty", Baku's Foreign Ministry said this week.
Azerbaijan requested the “full withdrawal of the Armenian armed units from the territories of Azerbaijan, the opening of transport and communication lines", its ministry said.
Armenia's Foreign Ministry repeated its demand for Azerbaijani troops to withdraw “from the sovereign territory of Armenia”, to release prisoners of war and to introduce “international mechanisms for controlling the situation on the border”.
Mr Blinken also praised steps the countries were taking to exchange prisoners of war.
The two foreign ministers last met for US-mediated talks with Mr Blinken on September 20 in New York.
Agence France-Presse contributed to this report
