PM Netanyahu earlier called on Benny Gantz to join him in a unity government. Israelis face with the prospect of a third election two days after unprecedented repeat polls left the country's two main political parties deadlocked.
Benny Gantz, Israeli Prime Minister Benjamin Netanyahu's main opponent in the country's general election, said on Thursday he should be prime minister in a broad unity government.
Gantz spoke to journalists after Netanyahu called for them to join together in a unity government, as results from Tuesday's vote showed neither with an obvious path to form a majority coalition.
"The public voted clearly in favour of unity," Gantz said.
"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 leader of the right-wing Likud voiced disappointment at his election challenger's rejection of his offer to discuss forming an Israeli unity government but said he remained open to talks.
"I was surprised and disappointed by the fact that, as of now, Benny Gantz still refuses my call to meet," Netanyahu said on Twitter. "Gantz, my offer that the two of us meet stands. It's what the public expects of us."
Netanyahu had earlier called on Gantz to join him and his traditional allies in a unity government.
"Throughout the campaign, I called for a right-wing government, but unfortunately, the election results show that's not possible," Netanyahu said in a video statement. "Therefore, there is no choice but to form a broad unity government."
"We cannot and there is no reason to go to third elections," he said.
Netanyahu repeated the plea later on Thursday at a memorial for late former Israeli president Shimon Peres, where he and Gantz shook hands in their first public encounter since Tuesday's vote.
Israelis contend with prospect of third poll
Israelis were contending with the prospect of a third election on Thursday two days after an unprecedented repeat election left the country's two main political parties deadlocked.
While weeks of negotiations to form a coalition government lay ahead, conditions set by the parties could hobble the task within the allotted time, prompting a never-before held third election.
With nearly all votes counted on Thursday, the centrist Blue and White party stood at 33 seats in Israel's 120-seat parliament.
Netanyahu's conservative Likud stood at 31 seats.
"Everyone will need to get off their high horse to prevent elections for the third time," Likud lawmaker David Bitan told Israeli Army Radio.
"Blue and White's desire for a unity government under their terms will not work."
Neither party can form a government of at least 61 seats without the support of the election's apparent kingmaker, Avigdor Lieberman of the Yisrael Beitenu party. His insistence on a secular government would force out Netanyahu's traditional allies, the country's two ultra-Orthodox parties and another nationalist-religious party.
Benny Gantz's Blue and White has pledged not to sit in the same government as Netanyahu, as the long-serving Israeli leader is expected to face indictment in a slew of corruption scandals. The fiercely loyal Likud is unlikely to oust Netanyahu.
Both parties were meeting with allies in the vote's aftermath and the focus will soon shift to President Reuven Rivlin, who will consult with all parties in the coming days and select the candidate who he believes has the best chance of putting together a stable coalition.
The candidate has 42 days to do so and if he fails, the president can give another candidate 28 days to form a coalition.
If that fails, the president can assign another parliament member the task of building a government or he can call new elections, something that has never happened.
Speaking at the Peres memorial, Rivlin promised he will do everything in his power to prevent a third election.
The deadlock follows the second Israeli elections this year, which were called because Netanyahu failed to cobble together a coalition following the April vote.
Israelis endured a caustic campaign that saw a combative Netanyahu fighting for his political survival amid the recommendation by Israel's attorney general to indict him on charges of bribery, breach of trust and fraud pending a hearing in early October.
Netanyahu had sought an outright majority with his allies in hopes of passing legislation to give him immunity from the expected indictment, which would otherwise increase the pressure on Netanyahu to step aside.
The vote was largely seen as a referendum on Netanyahu, who this summer surpassed Israel's founding prime minister to become the country's longest-serving leader.
During the campaign, Netanyahu cast himself as a seasoned statesman who was the only candidate able to steer Israel through a sea of challenges.
Gantz, a former army chief, tried to paint Netanyahu as divisive and scandal-plagued, offering himself as a calming influence and honest alternative.
Despite the scorched earth campaign that saw Netanyahu thrash institutions like the media, the police and the electoral committee – and which was tinged with anti-Arab rhetoric – the long-time leader failed to secure the resounding victory he needed to guarantee his political survival and perhaps save himself from a formal indictment.