The Middle East quartet discussions -- a dinner Thursday night and Friday's formal session -- are designed to show international backing for indirect talks between Israel and the Palestinians that the United States announced last week.
However, the launch of negotiations has been marred by a rare, public U.S.-Israeli dispute over Israel's plan to build 1,600 homes for Jews in a part of the occupied West Bank it annexed to Jerusalem.
Clinton has described the announcement -- made while U.S. Vice President Joe Biden was in Israel last week -- as insulting.
She had made a series of demands of Israeli Prime Minister Benjamin Netanyahu on the housing project itself and on showing his commitment to the indirect peace talks that the Israelis and Palestinians agreed to only last week.
U.S. State Department spokesman P.J. Crowley told reporters that Netanyahu had yet to telephone Clinton with his response, a step that he said the United States wanted before its peace envoy George Mitchell returns to the Middle East for a trip he has repeatedly put off.
(Additional reporting by Conor Sweeney, Steve Gutterman and Dmitry Sergeyev; editing by Guy Faulconbridge and Mark Trevelyan)