“We both agreed to do that homework and meet again in New York around the time of the U.N. General Assembly in order to see if it is possible then to find a date for that conference, much of which will obviously depend on the capacity to have success here in the next days″ on the subject of the chemical weapons, Mr. Kerry said. It was not clear if their Geneva meetings would wrap up Friday or continue into Saturday.

As the deliberations went on, Kofi Annan, the former United Nations Secretary General and prior Syrian envoy, also conferred separately with Mr. Kerry and Mr. Lavrov.

“These are fast-moving developments,” said Mr. Annan. “And I hope we are going to see further movement on the issue.”

“Hopefully at the end of the day we will come up with a proposal that deals effectively with the chemical weapons, gets people back to the table to seek political settlement and improve the humanitarian condition for the people of Syria.”

The State Department announced that Mr. Kerry would also be traveling to Jerusalem on Sunday to meet with Benjamin Netanyahu, the Israeli prime minister. Mr. Kerry met recently in London with Mahmoud Abbas, the president of the Palestinian Authority, and one purpose of his meeting in Israel is to discuss the Middle East peace talks.