The meeting was the first direct talks between Azeri and Armenian officials since deadly border clashes this month.
Armenia and Azerbaijan agreed to a ceasefire last week, ending two days of violence linked to a decades-old dispute between the two countries over Karabakh. The clashes, which each side blamed on the other, left more than 170 soldiers dead.
Convening Armenia's Ararat Mirzoyan and Azerbaijan's Jeyhun Bayramov on the sidelines of the United Nations General Assembly, Blinken emphasized the need to prevent further fighting and return to the peace process, State Department spokesperson Ned Price said in a statement.
"They discussed next steps, and the Secretary encouraged the sides to meet again before the end of the month," Price said.
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