Israeli Foreign Minister Tzipi Livni wrote in a private note captured by cameras on Sunday that her centrist Kadima party would not join any coalition government headed by right-wing Likud leader Benjamin Netanyahu.

The note, which Livni handed to outgoing Prime Minister Ehud Olmert of Kadima at the weekly cabinet meeting, set the battle lines in what could be weeks of political bargaining after Israel's inconclusive election last Tuesday.

Shortly after polls closed, both Livni and Netanyahu laid claim to the premiership, deepening uncertainty over the course Israel will follow after last month's Gaza war and in peace negotiations with the Palestinians.

Kadima won 28 seats in the 120-member parliament to Likud's 27, but a strong rightist bloc that emerged in the vote appeared to give Netanyahu the edge in putting together a governing majority.

"I have no intention of being in a unity government headed by Bibi -- and don't hint that," Livni, using Netanyahu's nickname, said in the note chiding Olmert, who was reported to have urged her to join a broad Likud-led coalition.

Television cameras are allowed to film the start of Israeli cabinet meetings, and they caught Livni writing the note. Its text could be read clearly when the paper was shown on TV news programmes.

Later, in broadcast remarks to Kadima legislators, Livni said the party deserved to lead Israel, but left open the possibility it would go into opposition.

"You don't have to be a mathematical genius to understand that 28 seats are more than 27," she said.

"We will continue to serve the public, either by forming the government, as the public chose, or if need be, in the opposition," Livni said.

Once election results become official on Wednesday, President Shimon Peres will begin consultations with party leaders to help determine whom he should pick to try to form a governing coalition.

The party leader he chooses will have 42 days to put together a government.