Three projections gave Mr Netanyahu's right-wing Likud party 36 or 37 seats, and Mr Gantz's centrist Blue and White alliance between 32 and 34.
However, the polls suggested Likud and its right-wing allies might fall just short of a majority in parliament.
Monday's election was Israel's third in less than a year.
Neither of the two main party leaders was able to command a majority in the 120-seat parliament following the last two rounds.
Mr Netanyahu, 70, is Israel's longest-serving leader. He is seeking a record fifth term, having been in office from 1996 to 1999 and again from 2009.
The election took place two weeks before the prime minister is due in court to face corruption charges, which he denies.
The exit polls put Mr Netanyahu within touching distance of forming a coalition government.
They aren't the real results; we'll have to wait many more hours for those.
And have one caveat in mind: Mr Netanyahu couldn't form a government with 60 seats for the right-wing bloc last April, leading to a year of political paralysis.
But he's already declaring victory: an important psychological part of fending off continuing calls to step aside over his corruption trial due to start later this month.
Meanwhile, the exit polls spelled bitter disappointment Mr Gantz.
At his party's election night HQ in Tel Aviv the spotlights swirled over a nearly empty hall floor. I could find only two party activists to talk to, who suggested the game wasn't over yet. Wait for the full results, they said.
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