For the first time, Netanyahu has clearly hinted in closed forums that if Kadima failed to join the government, he would work to split the party.
"I am determined to try to expand the coalition base at this time in the face of the Palestinian refusal and the various threats," the prime minister said.
"I am determined to do this, and my efforts won't stop even if Livni says no. I am serious in this intention of mine. I would be very happy to see her join, but I have no plans to give up on the attempt to expand the coalition base," he stressed.
Sources close to Netanyahu say that the offer made to Livni is a serious one. "This isn't a maneuver," one of them noted. "If she asks to join the narrow cabinet forum or other small forums, all the ways to let her influence will be found."
The prime minister's associates also say he does not plan to wait too long and enter long coalition negotiations, as the current political situation is not similar to the situation after the elections and there is now a stable government and loyal partners which Netanyahu does not wish to hurt.
Shortly after Netanyahu and Livni's meeting on Thursday, sources close to the prime minister told Ynet that despite his claims that he is serious in his intention to get the Kadima chairwoman to join the government, the offer itself is part of his ongoing attempt to split her party.
The Kadima Council convened Thursday evening to discuss the internal situation, and Livni was warmly welcomed by her party members. As for Netanyahu's offer, she clarified, "I am not slamming the door, but I will not be part of a game of small politics."
At this stage, it is unclear whether the attempt to divide Kadima will be executed in the near future or whether the process has been somewhat slowed down. Kadima sources estimate that Netanyahu has failed in his attempts and that he does not have seven Kadima MKs at this time who will take part in such a move.
Arab MK next opposition leader?
Meanwhile, following Netanyahu's offer to Livni, MKs have begun engaging in the question of who will be the next opposition leader if Kadima joins the government.
The law states that the opposition chairperson is the Knesset members from the biggest opposition faction. But if Kadima enters the coalition, the opposition will have three factions with the same number of members: United Arab List-Ta'al, Hadash and National Union.
In such a case, the law states that the opposition leader will be a member of the faction which won the highest number of votes in the elections, unless more than half of the opposition members choose a different MK.
As United Arab List-Ta'al got the highest number of votes out of these three parties, one of its members – perhaps MK Ahmad Tibi or MK Ibrahim Sarsur – is expected to become Israel's next opposition chairman.
It should be noted that the opposition leader in Israel has a special status. The law states that the prime minister must hold a meeting with the opposition leader at least once a month to brief him or her on current affairs. In addition, the opposition chairperson may speak at the Knesset immediately after the prime minister and is given a special place in state ceremonies attended by the prime minister.
Attila Somfalvi and Amnon Meranda contributed to this report