Israeli-Arab lawmakers have recommended that the former army chief Benny Gantz should become prime minister.
Last week's election put the incumbent leader Benjamin Netanyahu neck and neck with Mr Gantz, and the two are now vying to build a governing coalition.
Joint List, the bloc of Arab parties that came in third, says it wants to oust Mr Netanyahu from power.
This is the first time since 1992 that an Arab political group has issued an endorsement for prime minister.
This was Israel's second general election of the year. After the first, in April, coalition talks fell apart and a snap poll was called.
Faced with yet another deadlock, Israel's president Reuven Rivlin has recommended the new government includes both Mr Gantz's Blue and White Alliance, and Mr Netanyahu's Likud party.
Mr Rivlin has said he will do everything he can to avoid a third general election in Israel this year.
Aymen Odeh, leader of Joint List, told President Rivlin the alliance's priority was to prevent Mr Netanyahu from serving another term.
Joint List won 13 seats in the election. If Mr Gantz had the endorsement of all 13 seats, he would still fall short of the 61 seats needed for a majority in the 120-seat legislature.
This is a significant exercise of political power by Israel's Palestinian citizens.
President Rivlin is consulting party leaders about whom he should ask to lead the country after last week's inconclusive election results. The Arab parties put in a strong showing, becoming the third largest force in the legislature.
Their support will not give Benny Gantz and his Blue & White alliance a majority, but it will give him a boost in negotiations about who gets the first chance to form a government. Read More – Source