On 4 January 2021, Babayan was appointed the Minister of Foreign Relations taking over from Masis Mayilyan.

[citation needed] Since 2004, Babayan has been employed by the Artsakh University as a lecturer in political science, geopolitics.

[citation needed] In parallel with these positions, he was also held positions in government ministries of the Artsakh Republic including the Ministry of Foreign Affairs of the (2000 - 2001); the Presidential Planning Group (2001 - 2015); Assistant to the President (2005 - 2007); Head of the Central Information Department of the Office President (2007 - 2021).

In his capacity as Foreign Minister, he has sent letters to the United Nations, the Council of Europe and the co-chairs of the OSCE Minsk Group highlighting the illegal detention of Armenian servicemen and civilians in the Republic of Azerbaijan.

[citation needed] Following the 2023 Azerbaijani offensive in Nagorno-Karabakh on 19 and 20 September and the capitulation of Artsakh, Babayan announced his departure to Azerbaijani-controlled Shusha and his surrender to the Azerbaijani authorities, adding that "my failure to appear, or worse, my escape, will cause serious harm to our long-suffering nation, to many people, and I, as an honest person, hard worker, patriot and Christian, cannot allow this.