Both men claimed victory after the exit surveys were released by Israel's three main television stations following the closure of polling places at 1900 GMT.
Exit polls have proven to be unreliable in past Israeli elections.
The exit polls put Netanyahu's Likud with between 33 and 36 seats in the 120-seat parliament, while Gantz's Blue and White had either 36 or 37.
A combination of Netanyahu's Likud and smaller right-wing parties allied to him had between 60 and 66 seats, according to the exit polls.
Gantz's Blue and White alliance along with other smaller parties had between 54 and 60 seats, the polls showed.
"The right-wing bloc led by Likud won a clear victory," Netanyahu said in a statement.
"I thank the citizens of Israel for the trust. I will begin forming a right-wing government with our natural partners tonight."
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A statement from Gantz and the co-leader of his alliance, Yair Lapid, said "we won!"
"These elections have a clear winner and a clear loser," it said.
"Netanyahu promised 40 seats and lost. The president can see the picture and should call on the winner to form the next government. There is no other option!"
The vote had long been expected to be close and lead to frantic negotiations to form a coalition, even with Netanyahu facing potential corruption charges.
Turnout among Palestinians in Israel was especially low, with only 20 percent taking part amid calls for boycott following anti-Arab propaganda during the election campaign.
Netanyahu's Likud party provided right-wing activists with 1,200 hidden cameras "to monitor" Arab polling stations - a move that prompted Israel's Central Elections Committee to file a police complaint.
At 0800 GMT, police announced that they had discovered dozens of cameras at polling stations - some of hidden - in Palestinian-majority cities in Israel including Nazareth, Reineh and Tamra.
Yet, Palestinian parties remained optimistic despite low voter turnout.
"We are certain that we will pass the electoral threshold; according to our data, the voter turnout in the Arab sector was above 50 percent," United Arab List-Balad Chairman Mansour Abbas said.
"We should not forget that the exit polls ended at 8 P.M., so in the last two hours, there was a significant rise in the percentage of voters and support for the two Arab slates."
Final official results were not expected until early on Wednesday.
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