Benjamin Netanyahu, the leader of Israel's right-wing Likud party, has won the backing of a leading far-right party for his bid to become PM.
Yisrael Beiteinu leader Avigdor Lieberman said he wanted to see a "wide" coalition government taking in the three largest parties.
But Mr Netanyahu's rival for PM, Tzipi Livni, indicated she would prefer opposition to a unity government.
The process follows an inconclusive general election on 10 February.
President Shimon Peres is holding consultations with Israeli political parties to determine who to task with forming a government.
This is typically the party with the most seats, which would be Kadima, which beat Likud by 28 seats to 27.
But nationalist and religious parties, natural allies of Likud, also did well in the election.
With the support of Mr Lieberman, Likud can in theory now count on the support of 65 of the Israeli parliament's 120 members, putting it in a stronger position to form a government.
ELECTION RESULTS
# Kadima: 28 seats
# Likud: 27 seats
# Yisrael Beiteinu: 15
# Labour: 13
# Shas: 11
# United Torah Judaism: 5
If Mr Netanyahu is invited to form a government he will have six weeks to sew up a coalition.
'Wide' government
Israel Army radio reported Mr Lieberman telling Mr Peres that he supported the Likud leader as prime minister but "only as part of a wider government".
"We are not talking of a government with a restricted majority. To govern the country, we need a government with the three largest parties - Likud, Kadima and Yisrael Beiteinu.
"Netanyahu will be prime minister, but it will be a Bibi-Livni government," said Mr Lieberman, using Mr Netanyahu's widely-used nickname.
But Ms Livni implied she would prefer to sit in opposition than in a unity government with Mr Netanyahu and Mr Lieberman:
"Today, the foundations were laid for an extreme right wing government headed by Netanyahu. This is not our way and this is not our place to be," she said in comments to Kadima members circulated by the party.
"We were not elected to legitimise this extreme right government and we must form an alternative of hope and go to the opposition," she said.
Kadima campaigned on election pledges to continue peace talks with the Palestinians, while Mr Netanyahu stands further to the right and has opposed the negotiations.
Ms Livni's party had proposed a power-sharing deal with Likud similar to the one in 1984 which saw the leaders of Likud and Labour each hold the post of prime minister for two years.
Mr Lieberman did not make clear what he would do if Kadima refused to join a unity government.
Mr Peres is expected announce his decision on who should form a government in the next few days.
The 10 February election was called after Prime Minister Ehud Olmert handed in his resignation in September after being questioned by police over a series of corruption scandals. He has denied any wrongdoing.
Mr Olmert has stayed on as acting premier.
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