"During the elections, I called for the establishment of the right-wing government", said Netanyahu in a statement.
As Euronews reported, "Netanyahu had called elections to increase his majority, but the gamble spectacularly backfired".
"Benny, we need to put in place the widest possible unity government today". He also said, "the process of building a government has begun, and we will not be dictated to".
If such an offer had been approved by Mr Gantz, Israel could be governed by a broad unity government.
Moshe Yaalon, a senior leader from Gantz's centrist Blue and White Party, announced, "We will not enter a coalition led by Netanyahu". Neither party, however, can muster a majority coalition of 61 seats with their smaller allies.
Earlier Thursday, Gantz dismissed Netanyahu's offer of a unity government that includes the religious and right-wing parties, insisting that the next coalition should have himself as prime minister, not Netanyahu, and be committed to liberal policies on religious issues.
There "is no choice" but to form a unity government, he said.More news: General Mills recalls Gold Medal flour for E. coli contamination
Liberman described the bloc of 56 seats of Likud, Shas, UTJ and Yamina, which united on Wednesday under Netanyahu's leadership, as the "bloc of Jewish law", and again called on Netanyahu to sit down with him and Gantz to form a government without any other parties.
"When there was no clear outcome from the Knesset elections, Shimon chose national unity. He and Yitzhak Shamir agreed to cooperate, to navigate Israel's path to safety", Netanyahu said in remarks at the service.
With Israeli media reporting 99 percent of votes counted in Tuesday's election, a Likud-led right-wing, religious bloc looked poised to control 55 of parliament's 120 seats, with up to 57 going to a centre-left alliance.
Tillerson said he supported a two-state solution between the Israelis and Palestinians - an idea unlikely to feature in a peace plan being led by Jared Kushner, Trump's son-in-law and adviser.
The responsibility for making it happens falls to you elected officials, especially the leaders of the major parties.
"We can not and there is no reason to go to third elections", he added.
Netanyahu asked Gantz on Thursday to join him in a unity government.More news: Michael B. Jordan’s Netflix Superhero Series Raising Dion Gets a Trailer
Israeli President Reuven Rivlin, who will select one of the party leaders to have the first crack at forming a new government, welcomed the emerging notes of cooperation and called the rivals to negotiate.
Gantz also wants to form a "broad ... national unity government". "Prime Minister, on joining that call this morning", Rivlin said in remarks at the Peres memorial service.
A unity government as seen in the past in Israel involves parties alternating at the head of government for a fixed period of time. The parties both lie on the right wing of the political spectrum, though Netanyahu has increasingly courted hard-right support.
Blue and White has repeatedly ruled out sitting in a government under Netanyahu, who is expected to face a criminal indictment in the coming months, pending a hearing.
Netanyahu and Gantz, a former military chief of staff, shook hands in their first public encounter since Tuesday's vote.
Professor Dan Avnon, Chair of the Political Science Department at Hebrew University in Jerusalem said the election results showed that the majority of Israelis wanted a "stable, normal and functioning democracy".More news: Panthers QB (foot) not at practice, Week 3 status unknown
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