With some 97% of votes counted, Prime Minister Benjamin Netanyahu's Likud and Benny Gantz's Blue and White party still appear on track to get 35 seats each, but Netanyahu has a clear path to forming a right-wing government.
Both sides claimed victory in the hours after the voting ended.
But a third exit poll predicted that the bloc would be tied with centre-left parties allied to Mr Gantz.
He said the administration "has been working on a set of ideas" for Middle East peace "that we hope to present before too long", adding that he hoped they would provide a basis for discussions on resolving the Israeli-Palestinian conflict. Gantz, who heads the centrist Blue and White Party, will likely have the support of the left-wing parties.
Both claimed victory last night after exit polls last night suggested Mr Netanyahu's right wing Likud party and Mr... He then thanked his supporters and reiterated his commitment to them as well as to citizens who did not vote for him.
The country's attorney general recommended charging him with bribery, breach of trust and fraud in three cases. "And we are the winners", Gantz told a victory rally shortly after midnight.
Final results were expected on April 11, with ballots for soldiers and other special categories of voters yet to be counted.
A close result in the election would put smaller parties in a powerful position, turning marginal political figures into kingmakers.
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According to Haaretz contributor Chaim Levinson, Benny Gantz and the Blue and White Party are also "among the losers", notwithstanding their impressive showing of projected 35 seats. But recent projections appear to be giving Likud a slight lead and in a stronger position to form a majority coalition in the 120-seat parliament. The president, whose responsibilities are mostly ceremonial, is charged with choosing a prime minister after consulting with party leaders and determining who has the best chance of putting together a majority coalition.
Netanyahu - some times known as King Bibi, the title of a 2018 documentary about him - tweeted that Trump had called him from Air Force One.
Netanyahu made a last-minute pledge ahead of the elections to annex settlements in the occupied West Bank, a move that could end remaining hopes for a two-state solution if done on a large scale.
As CNN discovered when it visited a stronghold of his party Likud, in the desert town of Beersheva several weeks ago, that message resonates strongly with many blue-collar Israelis.
In showcasing his close ties with Mr Trump during the race, Mr Netanyahu sought to tap into the president's popularity among Israelis, who delighted in his recognition of Jerusalem as Israel's capital in 2017 and the subsequent transfer of the USA embassy there from Tel Aviv.
He has sought to overcome Netanyahu's experience by allying with two other former military chiefs and ex-finance minister Yair Lapid to form his Blue and White alliance.
How do Israeli elections work? The prime minister even approved a billboard in Tel Aviv showing himself shaking hands with the president in order to tout their close relationship.
U.S. officials have so far only revealed vague outlines of what the plan might propose, but Secretary of State Mike Pompeo suggested it could break abruptly with precedent.