Prime Minister Benjamin Netanyahu's Likud party has claimed a surprise victory in Israel's election, Israeli media report.
Earlier exit polls had suggested a dead heat with centre-left Zionist Union.
With most votes counted, Likud is said to be on course to take 29 seats in the 120-seat parliament, the Knesset, with the Zionist Union on 24 seats.
If confirmed, this would indicate another governing right-wing coalition led by Mr Netanyahu.
Speaking after the polls closed, Mr Netanyahu said he had already spoken to the leaders of other right-of-centre parties about forming a new government.
In a speech to his jubilant supporters in Tel Aviv, Mr Netanyahu described Tuesday's vote as a "great victory" for Likud, which had trailed the Zionist Union in opinion polls in the run-up to the election.
Likud supporters celebrated after the exit polls were announced
Zionist Union had been ahead in the opinion polls
Mr Netanyahu said the result was achieved "against all odds".
He urged the leaders of what he described as Israel's "national camp" to create "a government without delay".
At the scene: BBC's Kevin Connolly, Likud HQ, Tel Aviv
The Likud activists were dancing and singing within minutes of the TV stations broadcasting their exit polls quite simply because they can see a relatively simple pathway towards the formation of another right-wing coalition.
It would involve Mr Netanyahu teaming up with the secularists of Yisraeli Beitenu and Kulanu, and adding the religious nationalists of Jewish Home and the parties that represent ultra-orthodox Jews like Shas.
The outline of a workable coalition can be seen much more easily from this vantage point than from the point of view of the leftist Zionist Union led by Yitzhak Herzog.
He campaigned well and if the exit polls are to be believed he polled pretty well too - but the coalition arithmetic simply doesn't look so good for him.
Speaking after the exit polls were published, Mr Herzog told his supporters 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."
When final results are known, President Reuven Rivlin will give the task of forming a government to a party leader who he thinks has the strongest chance of assembling a coalition.
Israel's form of proportional representation always produces smaller parties and coalition government, the BBC's Middle East editor Jeremy Bowen in Tel Aviv reports.
DivideMr Netanyahu could become Israel's longest-serving leader if he secures a fourth term.
No party has ever won an outright majority under Israel's proportional representation voting system.
Almost 72% of those eligible voted in the election, which ended at 22:00 local time (20:00 GMT). The turnout was four points higher than the previous election in 2013.
Israel's Channel 1 and Channel 10 both projected 27 seats each for Likud and Zionist Union, while Channel 2 gave Likud a one-seat lead, with 28 seats.
Sixty-one seats are needed in order to secure a majority.
The Joint Arab List, an alliance of Israeli Arab-dominated parties, has come third with about 13 seats, the exit polls suggested.
It has said, however, that it will not take any positions in government.
Mr Netanyahu had vowed not to allow the creation of a Palestinian state if he wins a fourth term, while Zionist Union has expressed support for a two-state solution and promised to repair relations with Palestinians and the international community.
Earlier exit polls had suggested a dead heat with centre-left Zionist Union.
With most votes counted, Likud is said to be on course to take 29 seats in the 120-seat parliament, the Knesset, with the Zionist Union on 24 seats.
If confirmed, this would indicate another governing right-wing coalition led by Mr Netanyahu.
Speaking after the polls closed, Mr Netanyahu said he had already spoken to the leaders of other right-of-centre parties about forming a new government.
In a speech to his jubilant supporters in Tel Aviv, Mr Netanyahu described Tuesday's vote as a "great victory" for Likud, which had trailed the Zionist Union in opinion polls in the run-up to the election.
Mr Netanyahu said the result was achieved "against all odds".
He urged the leaders of what he described as Israel's "national camp" to create "a government without delay".
At the scene: BBC's Kevin Connolly, Likud HQ, Tel Aviv
The Likud activists were dancing and singing within minutes of the TV stations broadcasting their exit polls quite simply because they can see a relatively simple pathway towards the formation of another right-wing coalition.
It would involve Mr Netanyahu teaming up with the secularists of Yisraeli Beitenu and Kulanu, and adding the religious nationalists of Jewish Home and the parties that represent ultra-orthodox Jews like Shas.
The outline of a workable coalition can be seen much more easily from this vantage point than from the point of view of the leftist Zionist Union led by Yitzhak Herzog.
He campaigned well and if the exit polls are to be believed he polled pretty well too - but the coalition arithmetic simply doesn't look so good for him.
Speaking after the exit polls were published, Mr Herzog told his supporters 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."
When final results are known, President Reuven Rivlin will give the task of forming a government to a party leader who he thinks has the strongest chance of assembling a coalition.
Israel's form of proportional representation always produces smaller parties and coalition government, the BBC's Middle East editor Jeremy Bowen in Tel Aviv reports.
DivideMr Netanyahu could become Israel's longest-serving leader if he secures a fourth term.
No party has ever won an outright majority under Israel's proportional representation voting system.
Almost 72% of those eligible voted in the election, which ended at 22:00 local time (20:00 GMT). The turnout was four points higher than the previous election in 2013.
Israel's Channel 1 and Channel 10 both projected 27 seats each for Likud and Zionist Union, while Channel 2 gave Likud a one-seat lead, with 28 seats.
Sixty-one seats are needed in order to secure a majority.
The Joint Arab List, an alliance of Israeli Arab-dominated parties, has come third with about 13 seats, the exit polls suggested.
It has said, however, that it will not take any positions in government.
Mr Netanyahu had vowed not to allow the creation of a Palestinian state if he wins a fourth term, while Zionist Union has expressed support for a two-state solution and promised to repair relations with Palestinians and the international community.
