Israeli Prime Minister Benjamin Netanyahu and his main challenger Benny Gantz were in a standoff over calls for a unity government on Thursday as election results put the premier's long tenure at risk.

In a major development following Tuesday's polls, Netanyahu said he preferred to form a right-wing coalition, but that the results showed it was not possible.

He urged Gantz to join him in forming a unity government instead, and the two men shook hands when they crossed paths at a memorial event later.

But on Thursday afternoon, Gantz made clear that he would have to be prime minister of a unity government, noting that results so far put his centrist Blue and White two seats ahead of Netanyahu's right-wing Likud.

Despite Gantz's slim lead, neither has an obvious path to forming a majority coalition, and the Blue and White leader has made several calls for a unity government since polls closed on Tuesday.

Netanyahu's stark admission followed an election which has threatened his status as the country's longest-serving prime minister -- one who also faces possible corruption charges in the weeks ahead.

"During the elections, I called for the establishment of a right-wing government," Netanyahu said in a video message.

"But unfortunately the election results show that this is not possible."

He went on to call on Gantz to form a "broad unity government today."

Speaking to journalists, Gantz said: "The public voted clearly in favour of unity.

"Blue and White has at the time I am speaking won 33 seats, while Netanyahu has not obtained a sufficient majority to form a coalition as he hoped."

The ex-military chief, who mounted his challenge to Netanyahu without any prior political experience, went on to say: "We will listen to everyone, but we will not accept mandates imposed on us."

"Blue and White, headed by me, has won the election. Blue and White is the largest party."

Netanyahu responded with a statement saying he "was surprised and disappointed that at this time Benny Gantz still refuses to respond to my call to meet."

'Loud and clear'

Israeli President Reuven Rivlin, who must choose who will form the next government, welcomed Netanyahu's call for a unity coalition.

He is due to begin consultations with political parties on Sunday to decide who should form the government.

"I hear, loud and clear, the voices calling for a broad and stable national unity government," he said at the memorial, held to mark the third anniversary of the death of veteran statesman Shimon Peres.

"And I congratulate you, Mr. prime minister, on joining that call this morning."

Netanyahu appeared to be seeking to seize momentum by announcing his intention to form a unity government and head off attempts to oust him.

Gantz has in the past sought to persuade members of the right-wing Likud to oust Netanyahu as party leader and form a unity government with Blue and White.

But there has so far been no signal that Likud members would be willing to do that, and in his speech following the closure of Tuesday's polls, Gantz made no such demand.

Official results have not been announced, but Israeli media have reported that Blue and White has 33 parliamentary seats and Likud 31 out of 120, with 97 percent of the votes counted.

'Schticks and tricks'

Ex-defence minister Avigdor Lieberman has emerged as a potential kingmaker, with the reported results showing his nationalist Yisrael Beitenu party with eight seats.

On Thursday, he again called for a unity government between his party, Blue and White and Likud, but gave no hint of who he would endorse as prime minister.

Netanyahu should "stop with the political exercises, shticks and tricks," he said of his former close ally turned nemesis.

"Let's sit down -- you, Benny Gantz and myself -- and establish a broad, liberal national government for the future of the State of Israel."

His "liberal" reference echoed his wish to exclude Israel's ultra-Orthodox Jewish parties, which he accuses of seeking to impose religious law on the secular public.

Israel's newly reunified Arab parties, running together under the Joint List alliance, have also emerged as an important force, with the reported results showing them with 13 seats -- the third-largest.

Joint List leader Ayman Odeh could potentially become the country's first-ever Arab opposition leader if a unity government between Blue and White and Likud is formed.

Rivlin's consultations beginning Sunday will be the second time he has held them since April.

Netanyahu suffered one of the biggest defeats of his political career after elections that month.

His Likud along with its right-wing and religious allies won a majority, but he failed to form a coalition and opted for a second election rather than risk having Rivlin choose someone else to try.