“Right now, the ceasefire is holding,” Mr Vance said at an event in Athens in the state of Georgia.
The US sees itself as a mediator in the talks between Russia and Ukraine.
Kyiv is refusing to cede the territories Russia demands, including those in the Donetsk region that Ukraine still controls.
U.S. Special Envoy Steve Witkoff and U.S. President Donald Trump’s son-in-law, Jared Kushner, also took part in the talks on ending the war in Ukraine.
Speaking aboard Air Force One on Sunday, Mr Trump told reporters the Iranian leadership had called him “to negotiate” a day earlier.
The White House has yet to confirm the meeting.
Trump in July gave Moscow a 50-day deadline to end the war.
According to the Hamas-controlled health authority in Gaza, 60,000 Palestinians have been killed in the conflict so far.
