Gantz had not yet responded, but he has repeatedly called for a unity government.
The prime minister acknowledged that he promised a right-wing government during the election, but said that "unfortunately, the results of the election showed it is not possible".
Secretary General of Palestine Liberation Organization (PLO) Saeb Erekat, for his part, told "Voice of Palestine" Radio that the initial results of the Israeli parliamentary elections showed that the competition was between two parties: one called for deepening the apartheid and the other called for keeping the situation as it is. "In the next few days, we will begin negotiations to form a strong, Zionist government and in order to avert a risky, anti-Zionist government", a tired looking Netanyahu told supporters in the Likud headquarters late Tuesday night. "The nation expects us, both of us, to demonstrate responsibility and that we pursue cooperation".
For Netanyahu, of course, this is also personal as he faces three corruption charges on which pre-trial hearings are about to commence soon. We are not permitted and there is no reason to go to a third election - I am against it.
Netanyahu could negotiate with Lieberman, a man who stood by his side during the previous government, but who also resigned and refused to sign up to Netanyahu's coalition after the last elections in April.
Netanyahu said he was "surprised and disappointed" and reiterated his call to Gantz to join him.
Though it is always hard to predict the future of politicians, and that too a politician as formidable as Netanyahu, it seems that we might be standing on the cusp of an important political moment in his political career and of Israeli politics.
Benjamin's Netanyahu coalition is six seats short of a majority in parliament.
After failing to form a coalition following April's election, Netanyahu called Tuesday's vote, only to see the country emerge with another political stalemate.
Neither party can form a government without the support of the election's apparent kingmaker, Avigdor Lieberman of the Yisrael Beitenu party.
The rival parties are no closer to forming a majority coalition, raising the possibility of negotiations for a unity government.
A center-left alliance passing the 61-seat threshold, then, would require Ultra Orthodox parties that traditionally ally with Netanyahu to instead sit with Blue and White, Labor-Gesher and the Democratic Union.
Gantz is a newcomer to politics.
Netanyahu's call for a broad government preceded a scheduled visit later on Thursday by outgoing US envoy Jason Greenblatt, an architect of President Donald Trump's as-yet unveiled plan for Israeli-Palestinian peace.
Palestinians, who seek a state in the West Bank and Gaza, with its capital in occupied East Jerusalem, have warned such a move will kill any hopes for peace.
With Israeli politics in flux, Netanyahu cancelled his annual speech at the U.N. General Assembly next week, a spokesman said on Wednesday about a visit that might have provided an opportunity to meet with Trump.
Foreign Minister Israel Katz will replace Netanyahu at the world body.