Prime Minister Netanyahu's office announced he will not travel to New York next week for the UN General Assembly, as previously planned. The decision came in the wake of election results, the office added.
Netanyahu failed to win a ruling majority in an election that produced a virtual tie between his right-wing bloc and a center-left grouping that would be led by former military chief Benny Gantz.
The outcome, according to almost complete results published on Wednesday, dealt a new blow to Israel's longest-serving leader who was already weakened by the inability to put together an administration after an inconclusive election in April.
But with coalition-building again key to forming a government, it could be days or even weeks before it becomes clear whether Netanyahu has been dethroned after a decade in power.
With around 90 percent of votes counted in Tuesday's election, the bloc led by Netanyahu's Likud party was more or less even with a likely grouping headed by Gantz's centrist Kahol Lavan party.
A Likud-led bloc looked poised to control 55 of parliament's 120 seats, with 56 going to a centre-left alliance, numbers falling short of a majority government of 61 lawmakers.
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A Likud spokesman said the leaders of right-wing factions met Netanyahu at the prime minister's office on Wednesday and pledged to work with him to form the next government.
The ballot's wildcard, former Defence Minister Avigdor Lieberman, emerged as a likely kingmaker as head of the secular-nationalist Yisrael Beitenu party, projected to capture nine seats.
Lieberman has been pushing for a unity government comprised of the biggest parties. He declined to back Netanyahu's bid to form a narrow right-wing and religious coalition after the April election, bringing about Tuesday's unprecedented repeat vote.