Benjamin Netanyahu's main challenger, Isaac Herzog, has disputed the prime minister's claim of victory in Israel's election, saying, "Everything is open".
"This result allows us to return to power," Herzog told supporters at his party's headquarters in Tel Aviv.
"We will wait for the real results ... everything is open", he said.
Israeli Prime Minister Benjamin Netanyahu said he had invited other right-wing politicians to join him in a coalition government "without delay".
"Reality does not take a break," Netanyahu said in a speech to supporters after two television exit polls gave Likud a narrow lead over his centre-left challenger in the ballot.
Challenger to Prime Minister Benjamin Netanyahu, Isaac Herzog has said that "everything is open" in the election results.
He responded to Netanyahu's tweet of a "major victory" for Likud in the election.
Official results are not expected to be released until at least Wednesday morning.
Israeli Prime Minister Benjamin Netanyahu has tweeted that his party has won "a major victory for the people of Israel".
The tweet, in Hebrew, read: "Against all odds: A great victory for the Likud, a major victory for the national camp led by the Likud, a major victory for the people of Israel."
No official statement on behalf of the Israeli Prime Minister has been released.
Against all odds:a great victory for the Likud. A major victory for the people of Israel!
Exit polls in Israel show that Prime Minister Benjamin Netanyahu's Likud party drew even with Isaac Herzog's Zionist Union in the election.
The polls, by Israel's leading television channels, suggest that the formation of the next government could be a serious challenge for both candidates.
Channel 10 and Channel 1 said Likud and the Zionist Union had secured 27 seats each in the 120-member Knesset.
But Channel 2 said that Netanyahu had eked out a narrow victory, winning 28 seats to 27 for Herzog.
Final results are expected early on Wednesday morning.
Israeli Labour Party leader Isaac Herzog, the man hoping to prevent Prime Minister Benjamin Netanyahu from becoming Israel's longest-serving leader, has cast his vote in the election for country's the next parliament.
Israeli Prime Minister Benjamin Netanyahu cast his vote in the election as polls opened this morning.
Palestinians in the occupied West Bank do not expect any changes to their conditions whoever wins power in next week's elections in Israel.
Whereas settlers in the are entitled to vote in the poll, Palestinians living in there have no such rights.
ITV News correspondent Geraint Vincent reports.