The meeting took place following Netanyahu's attempts to convince other Knesset members to "defect" to the Likud. However, according to Netanyahu's proposal, Kadima will be joining the government without receiving any portfolios.
"The prime minister met with the opposition chairwoman for about an hour and a half and briefed her on security and diplomatic issues," the PM's Office said.
"After presenting the issues at hand, the prime minister offered Ms. Livni to join a national unity government, in line with the model where Menachem Begin joined the government in 1967."
The offer, added the statement, came "in view of the national and international challenges Israel faces at this time.
"The prime minister told the opposition chairwoman that the basis for joining a national unity government is the premise presented in his Bar Ilan speech."
Sources close to the prime minister said he was heard telling close advisors that his offer was bona fide: "I made a serious offer and I expect a serious answer. The outline is clear and no coalitional negotiations will be held," he said.
According to the sources, Netanyahu stressed that he will not abide any political games and that he expected Livni's answer within a few days.
Livni, on her part, said that "if this is a genuine offer then, as I've said before, it is something to consider… However, this goes beyond the mutual understanding of threats. We have to explore this further and meet again.
"In any case," she added, "The final decision will be made by Kadima and not just by me."
Responses to the offer were not late in coming: Education Minister Gideon Sa'ar urged both Livni and Kadima to show "national responsibility" and accedes the PM'S request to join the unity government. According to Sa'ar, the decision must be based on "the security, social and national challenges facing the country."
MK Ronit Tirosh (Kadima) warned that if Livni's refusal would stem from the "wrong reasons" the party may split: "Kadima's rightful place is in the government… the party cannot remain in opposition and wait for the radical (elements) to topple the government, while Netanyahu fulfils Kadima's platform."
MK Dalia Itzik added: "I feel that Bibi's (Netanyahu) offer is not serious, and we must not be fooled into his spin."
Later Thursday, Netanyahu’s associates told Ynet that the PM’s offer to Livni is part of his effort to dismantle Kadima.
“The prime minister’s offer to Livni is not detached from the political move aimed at getting rid of Kadima, and in fact this is a complementary move aimed at providing a good pretext for senior Kadima officials who thus far did not express willingness to split the party,” one associate said.
“In any case, this situation marks success and a victory for Netanyahu,” a source intimately involved in the contacts between Bibi and Kadima officials said.
Later still, Livni said that if Netanyahu's offer was indeed meant to expedite Kadima's demise, she would have no part in it.
"I told Netanyahu that if his offer was part of the attempt to dismantle Kadima I won't be a part of his game… I'm not dismissing the offer and I will give it serious consideration," she said.
Amnon Meranda contributed to this report