Estimates by two Israeli broadcasters gave both sides 27 seats each in the 120-seat parliament, the Knesset.
Both would need support from other parties to form a governing coalition.
PM Benjamin Netanyahu described the vote as a “great victory” for his Likud party, which is credited with a better result than expected.
In a speech to his jubilant supporters in Tel Aviv, Benjamin Netanyahu said this was achieved “against all odds”.
Likud had trailed the centre-left Zionist Union in opinion polls in the run-up to the poll.
However, the centre-left Zionist Union dismissed what it termed “spin” from Likud as “premature”.
Yitzhak Herzog, head of the Zionist Union, told his supporters that he was confident of forming the next government.
“We have achieved an unbelievable achievement today.
“I will do all that I can in order to create a real socially-minded government for Israel.”
While the final results were not yet known, Yitzhak Herzog said: “I will do all that I can in order to create a real socially minded government for Israel.”
Final results are not expected until Wednesday morning, March 18.
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