Azerbaijani President Ilham Aliyev discussed his country’s troubled peace process in a phone call with U.S. Secretary of State Antony Blinken, Aliyev’s office said Friday.

Washington appreciates the progress in peace negotiations between Azerbaijan and Armenia, Blinken told Aliyev, according to the Azerbaijani presidential statement.

He assured Aliyev that the U.S. would continue supporting the Azerbaijani-Armenian normalization process and expressed the need to sign a peace treaty "as soon as possible."

Aliyev reminded Blinken that peace has been facilitated in the Karabakh region and that his government has proposed principles that form the basis for a peace treaty.

"As Azerbaijan, we will continue our efforts to take the normalization and peace process with Armenia to the next level," he told Blinken.

Welcoming the U.S. desire to contribute to the peace process, Aliyev said Armenia must end its territorial claims towards Azerbaijan in its constitution and other laws and regulations for the process to proceed.

Aliyev also argued it was time to dissolve the Organization for Security and Co-operation in Europe (OSCE) Minsk Group.

Established in 1992, the OSCE Minsk Group, chaired by France, Russia and the U.S., aimed to facilitate the resolution of the decadeslong Karabakh conflict.

Azerbaijan and Armenia are currently working to normalize their relations after Azerbaijan regained full control of the Karabakh province that had been under the illegal occupation of Armenia-backed ethnic Armenian separatists since the 1990s.

A six-week war in 2020 resulted in Azerbaijan liberating large parts of the breakaway region and in September 2023, Azerbaijani forces launched a lighting blitz that forced Karabakh's Armenian "authorities" to capitulate in negotiations mediated by Russian forces.

Since December, the sides have been struggling to begin negotiations on a peace treaty, key parts for which were demarcating borders and establishing regional transport corridors through each other's territory.

In a historic breakthrough, Armenia returned four border villages, which were seized in the 1990s, to Azerbaijan late last month. The sides also agreed on the new demarcation of 12.7 kilometers (almost 7 miles) of their border, returning the villages of Baghanis Ayrum, Ashaghi Askipara, Kheyrimli and Ghizilhajili to Azerbaijan.

Although the move sparked protracted protests in Armenia, it’s hailed as a move toward reaching a comprehensive peace agreement after years of fruitless talks mediated by Russia and Western countries.

The territory ceded back by Yerevan is strategically important for landlocked Armenia because it controls sections of a vital highway to Georgia.

Armenian residents of nearby settlements say the move could cut them off from the rest of the country and accuse Prime Minister Nikol Pashinyan of unilaterally giving back territory without getting anything in return.

Azerbaijan and Armenia still have other unresolved territorial disputes. These are mostly focused on enclaves that the two sides want the other party to relinquish control or provide access to.

Pashinyan said the sides were close to completing their peace treaty earlier this month but said Yerevan would not accept Baku’s demands that it change its constitution.

Aliyev has repeatedly demanded that Armenia change its constitution to remove an indirect reference to Karabakh independence before inking a peace deal.

Armenian media cited Pashinyan as saying that the insistence on constitutional amendments represented an attempt at "torpedoing" the peace process, even though he said the deal's prospects remained good.