Kerry "noted that this week is an opportunity to make additional progress and stressed that it is our intention to do so," according to a readout of the meeting by a senior State Department Official, speaking on background.
The official said Kerry and Zarif met for over an hour at a hotel and "agreed to meet further as needed while in New York."
The official said the two ministers also discussed the threat posed by the Islamic State in Iraq and the Levant (ISIL) terrorist group, Press TV reported.
The meeting comes as nuclear negotiators representing Iran and the Group 5+1 (Russia, China, the US, Britain, France and Germany) started a fresh round of talks on Tehran’s civilian nuclear work in New York last Friday.
The negotiations are expected to run until at least September 26 on the sidelines of the annual gathering of world leaders at the United Nations General Assembly.
Iran and the sextet are trying to work out a lasting accord aimed at ending the longstanding dispute over Tehran’s civilian nuclear activities.