Speaking at a virtual event held by the Atlantic Council think tank, Armenian Foreign Minister Zohrab Mnatsakanyan said he had "very productive" meetings with Pompeo.
Reiterating Azerbaijan's main condition for ending the fighting, Aliyev demanded promises that his country will be handed back control of Nagorno-Karabakh.
Storied Azerbaijani champion visits Bloomfield for Europa League duel with yellow-and-blue.
Russia has until now driven mediation efforts over Nagorno-Karabakh, a breakaway enclave within Azerbaijan that is controlled by ethnic Armenians.
Several hundred people have been killed in the fighting, which each side blames on the other, and there are fears of a humanitarian crisis.
Israel and Armenia have numerous historical reasons to be allies. Perhaps the most obvious is that both peoples have faced tremendous persecution for their faith and ethnicity.
The ceasefire was agreed on Saturday after a deal brokered by Russia a week earlier failed to halt the worst fighting in the South Caucasus since the 1990s.
"I am proud to be here myself, liberating lands which were conquered more than 30 years ago. My friends and I truly believe this."
The ambassador noted that Israel stands in solidarity with their Azeri friends, and offered to provide humanitarian aid to the country.