Benjamin Netanyahu's Likud party received less votes than Gantz's Blue and White coalition.
Israel's Arab-dominated Joint List party on Sunday backed Benny Gantz to form a new government, making his bloc of supporters larger than that of Benjamin Netanyahu, though still neither commanded a majority.
The Joint List, according to near final results, won 13 of the Knesset's 120 seats, making it the third-largest grouping.
With their support Gantz heads a center-left bloc of 57 seats compared to Netanyahu's right-wing bloc of 55. Former Defense Minister Avigdor Lieberman, whose party secured eight seats, has yet to back Gantz or Netanyahu.
Israel's president on Sunday began consulting with party leaders to discuss who should lead the country after no clear victor emerged from last week's election, suggesting Netanyahu's Likud join forces with its main rival.
Netanyahu's right-wing Likud failed, for the second time in five months, to secure a clear election victory. The centrist Blue and White party led by Gantz has a slight lead with nearly all votes counted.
Gantz has so far rebuffed Netanyahu's calls to join a unity government.
Near-final results show Blue and White will be the largest single party in the new parliament with 33 of the 120 seats, while Likud has won 31 seats, three less than it had before.
President Reuven Rivlin on Sunday began consultations with the parties about choosing a leader to put together a coalition.
In a meeting with Likud party leaders, Rivlin said it was up to the "two biggest parties, the first and second that are almost equal in size, to join forces ... so that you together manage and establish a system that brings a stable government."
"This is what the people want. None of us can ignore that," he said.