The centrist Blue and White alliance of former military chief Benny Gantz is projected to win between 32 and 34 seats, and Prime Minister Benjamin Netanyahu's right-wing Likud party 31 to 33 seats, the BBC reported on Tuesday citing the exit polls' figures.
Yisrael Beiteinu party leader Avigdor Lieberman may end up being kingmaker.
Netanyahu called the snap vote after failing to form a governing coalition in the wake of an election in April.
Negotiations on the formation of a new coalition are expected to start as soon as the preliminary results come on Wednesday morning.
The exit poll of Israel's public broadcaster Kan projected that Likud and Blue and White would each win 32 seats in the 120-seat Knesset.
In third place was the Israeli Arab Joint List with 12 seats; followed by Lieberman's secular nationalist Yisrael Beitenu party with 10; the right-wing Yamina party with seven; the ultra-Orthodox Shas and United Torah Judaism parties with nine and eight respectively; and the left-wing Democratic Union and Labour-Gesher alliances with five each.
Channel 12 News put Blue and White ahead with 34 seats and Likud with 33, while Channel 13 News predicted that Blue and White would win 33 seats and Likud 31.
There was a muted response at Likud's election night headquarters in Tel Aviv as the exit polls were released. Hundreds of chairs for party supporters remained empty, as activists were kept outside the hall and leaders digested the numbers.
A Likud spokesman noted that Israeli exit polls had got things wrong in the past. Last time, they underestimated the number of votes for Likud and also for some of the religious parties allied to Netanyahu.
"There is no point starting to work out a coalition based on these numbers as they will change," Eli Hazan said.
But Blue and White was "cautiously optimistic" that Israel would get new leadership, spokeswoman Melody Sucharewicz told the Times of Israel.
( With inputs from IANS )