Rivlin, who began consulting with party leaders on Sunday to discuss who should lead the country after no clear victor emerged from Tuesday's election
Israel's Arab-dominated Joint List party moved on Sunday to back the centre-left bloc of Benny Gantz, who is challenging Prime Minister Benjamin Netanyahu's right-wing alliance, to form a new government.
With final results all but in, neither Gantz nor Netanyahu command a majority in parliament, so the Arab List's decision to end its usual policy of withholding support for any candidate in the wake of elections could nudge President Reuven Rivlin to ask Gantz to form a government.
Rivlin, who began consulting with party leaders on Sunday to discuss who should lead the country after no clear victor emerged from Tuesday's election, suggested Gantz and Netanyahu join forces, though it is uncertain who would be the senior partner.
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 ex-armed forces chief Gantz has a slight lead with nearly all votes counted.
No party drawn from the 21% Arab minority has ever been part of an Israeli government. But an increased turnout saw the Joint List win 13 seats, making it the third largest grouping.
This would provide an outlet to voice Arab complaints of discrimination in Israeli society and give a bigger platform to Arab parties which differ markedly with those drawn from the country's Jewish majority on many political issues.
"We want to bring an end to the era of Netanyahu, so we recommend that Benny Gantz be the one to form the next government," party head Ayman Odeh told Rivlin on Sunday as part of consultations to form a new government coalition.
Joint List's support does not mean it will sit in the governing coalition, but its backing gives Gantz's centre-left bloc 57 seats, compared to Netanyahu's right-wing bloc of 55.
Netanyahu denounced the Arab party support of Gantz. He said it meant only two choices - "a minority government that leans on those that reject Israel as a Jewish, democratic state," or a "broad national government."
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.
In a meeting with Likud party leaders on Sunday, 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.
The president's role is largely ceremonial, but it includes consulting with factions and choosing which party leader has the best chance at forming a coalition.
There were only narrow differences in the two main parties' campaigns on many important issues during the campaign. An end to the Netanyahu era would be unlikely to bring significant changes in policy on relations with the United States, the regional struggle against Iran, or the Palestinian conflict.
Netanyahu and Gantz are now seeking other potential coalition allies, prominent among whom is the far-right former defence minister Avigdor Lieberman. He secured eight seats for his Yisrael Beitenu party, making him a potential kingmaker.
Lieberman on Sunday reiterated his call for a unity government and said he would not recommend either candidate in his meeting with Rivlin.