Representatives of the centrist Blue and White party and the right-wing Likud party met in Ramat Gan, outside Tel Aviv.
The meeting came a day after Benny Gantz, leader of Blue and White, met with Prime Minister Benjamin Netanyahu’s Likud party for the first time since the elections at the request of President Reuven Rivlin.
At the end of the meeting, Gantz and Netanyahu issued a joint statement saying they had agreed to launch negotiations on a possible unity government.
The two have agreed to meet again on Wednesday.
In last Tuesday’s voting, both parties did not gain enough votes to form a majority government in the 120-seat parliament, with 33 seats for Blue and White party and 31 for the Likud.
Netanyahu has refused to step down, calling for a broad unity government under his leadership.
Leaders of Blue and White have repeatedly said during their election campaign that they will not join a government under Netanyahu’s leadership as long as he has corruption cases against him.
Netanyahu is a suspect in at least three separate criminal cases of bribes, fraud and breach of trust. Attorney-General Avichai Mandelblit already said he intends to charge Netanyahu, pending a hearing that is expected to take place in two weeks.
Israeli President Reuven Rivlin on Sunday began consultations with all elected parties before taking a decision on the person who will be tasked with forming Israel’s next government amid post-election political stalemate.
The two-day round of consultations began with a meeting with Benny Gantz, leader of the Blue and White party. On Tuesday’s elections, the centrist party won a narrow victory over Prime Minister Benjamin Netanyahu’s right-wing Likud party.