Officials from both sides said the agreement was reached at a short meeting between Sharon and Peretz on Thursday aimed at breaking up the ruling coalition and setting a date for early elections.
Peretz said that he hoped an exact date would be set by Monday, when parliament is expected to discuss bringing forward elections, which had originally been scheduled for November 2006.
Peretz, who ousted the veteran deputy premier Shimon Peres in a leadership election last week, has said he wants elections as soon as possible.
Sharon, meeting Peretz for the first time since the Labour leadership vote, has said that he favours holding an election as early as February. Labour’s departure would leave Sharon without a parliamentary majority.
In an interview published on Thursday, Sharon also indicated he saw no point in dragging out the process, saying he wanted to avoid any diplomatic stalemate.
“In the intricate and complex reality that the country is in, I have no intention of heading a minority government for long months,” Sharon told the Yediot Aharanot daily.
“I did not think the elections should be moved up, but as soon as it became clear to me that the existing political establishment was coming apart, I reached the conclusion that the best thing for the country is to hold an election campaign as soon as possible.”