Prime Minister Benjamin Netanyahu asked opposition leader Tzipi Livni, the chairwoman of Kadima, on Thursday to join a unity government. Livni did not immediately reject the offer, and added that if the offer is real "I always said that it is up for discussion."

Livni clarified that any decision regarding Kadima's moves will be taken by the party after thorough discussion and not by her alone.

Netanyahu told Livni that Kadima's addition to the government was crucial in light of the local and global challenges facing Israel today.

During their meeting, which lasted about 90 minutes, Netanyahu briefed Livni on political and security issues on the government's agenda, telling her that the basis for joining a unity government would be principles of peace and security that he outlined in his foreign policy speech at Bar Ilan University in June.

Netanyahu offered Livni to include four Kadima members in inner cabinet discussions, should Kadima join the proposed unity government, but he didn't offer ministerial portfolios.

The meeting between the prime minister and the opposition leader comes on the tail of Livni's accusation earlier Thursday that Netanyahu was trying to split Kadima, currently embroiled in a proxy war over the faction's leadership.

Kadima No. 2 Shaul Mofaz on Thursday demanded that Livni take the party to primary elections, telling reporters after their afternoon meeting that he hoped she would "listen to others, for once" and keep the party from breaking up.

The rift at the top of Kadima worsened on Wednesday, after MK Mofaz lashed out at Livni, saying it was her lack of leadership that has reportedly led 14 of Kadima's 27 MKs to start negotiations with Likud about moving to that party.

Mofaz met Livni at her north Tel Aviv home on Thursday afternoon, hours before the faction's council was to convene to discuss the future of the party.

Livni told Mofaz during the talks that she feared Netanyahu was "trying to split Kadima. It's on the table and it's a fact." She urged Mofaz, along with other senior members of the party to do everything possible to keep Netanyahu from "weakening Kadima."

Party unity must come before everything else, Livni declared.

A Mofaz associate quoted him as saying on Wednesday that the possible migration of Kadima members away from the party indicated that a "group of MKs doesn't acknowledge Livni's leadership, and they have doubts about her ability to lead in general."

"The fact that not a year has passed since the election and people are already looking to flee Kadima is a clear challenge to her leadership and [indicates] that they don't see her as a future leader."

Wednesday night, MK Eli Aflalo became the first Kadima MK to officially announce that he intended to leave Kadima, though he has yet to decide whether to join Likud or start his own faction. "You took Kadima too far left and betrayed me; I don't believe you anymore," Channel 1 television quoted him as saying.

In conversations with associates Mofaz blamed the threatened desertions on Livni's mistakes - first and foremost her failure to form a new government last year after Ehud Olmert's resignation as prime minister and her subsequent election to replace him as party leader, and then her refusal to join Prime Minister Benjamin Netanyahu's government after the elections, for what Mofaz termed personal reasons.

But publicly he has kept silent, not wanting to be seen as the one who split the party.

Mofaz believes these latest developments will necessitate moving up the Kadima primary to sometime next year. When he tried to push up the primary date a few months ago, he failed in part because this would require changing the party's bylaws, which call for the primary to be held three months before a general election. Changing the bylaws is difficult, because they give great power to the party chair. Today, however, Moaz believes the idea will enjoy such sweeping support among Kadima activists and MKs that the change will be possible.

But Livni insisted to her associates Wednesday that the new developments are no grounds for moving up the primary.

Livni also slammed Netanyahu on Wednesday over his courtship of Kadima MKs. That prompted associates of both Mofaz and Netanyahu to accuse her of hypocrisy, saying she herself has been busy trying to woo Labor MKs to Kadima.

"Livni's problem isn't Netanyahu, but her own lack of leadership," added one of the premier's senior associates. "Someone who isn't capable of running her party shouldn't come crying to the prime minister."

Kadima's governing council will meet Thursday to discuss the threatened desertions, and the meeting is expected to be stormy. Mofaz does not intend to speak, but he has made his views clear to party members.

Mofaz, meanwhile, has been trying to prevent any desertions. In the past few days he has met with almost every Kadima MK rumored to be talking with Likud. Some denied it; others said they were considering it.

Nonetheless, it will be harder for Netanyahu to find seven Kadima lawmakers who wish to leave the party, the mandatory number required in order to split off without Livni's approval, after MKs Israel Hasson, Jacob Edery and Arie Bibi announced on Thursday that they had no intention of deserting. They had earlier been seen as leaning toward such a move.

Mofaz is particularly anxious because some of those who are reportedly talking with Likud are his supporters - people he views as the basis of a future leadership bid.

But Mofaz was not the only one attacking Livni on Wednesday. A former Kadima minister, for instance, also blamed her for the situation, saying she had ignored her fellow MKs and run the party undemocratically, and now, her colleagues are taking revenge.

Responding to such criticisms, Livni told associates, "I'm aware of my flaws and am working to correct them." She has met with many Kadima MKs over the past few days and told them she understands that she needs to consult her party colleagues more, and this is an opportunity for change.

But some in Kadima insisted that the MKs who are thinking of leaving are marginal. "No one in Kadima would cry if they decided to quit," said one.