Blinken commended the recent advancements, including the August 30, regulation on border delimitation, and reiterated the US commitment to supporting a durable peace in the region.
The two leaders held the discussions over the phone on Monday.
Aliyev underscored that peace is already established, attributing this to Azerbaijan's efforts, reports Xinhua news agency.
He emphasised Azerbaijan's role in creating new realities based on justice and international law.
The Azerbaijani leader also highlighted the need for Armenia to renounce territorial claims in its constitution and called for the dissolution of the OSCE Minsk Group, which he considers outdated.
The discussion also addressed Azerbaijan's role in hosting COP29, with Blinken expressing strong US support and praising bilateral cooperation. Aliyev expressed the hope for significant consensus on climate finance at the conference.
The two sides also reviewed Azerbaijan-US relations during their conversation.
