Following their first meeting since then, Livni stressed that the two talked "only about foreign affairs of the State of Israel."
The Prime Minister's Office, for its part, said in a statement Sunday that Olmert and Livni "agreed to continue working together as part of the government headed by Ehud Olmert."
The two also agreed to continue working on the promotion of the diplomatic process.
Peres: I won't work to oust PM
Vice Premier Shimon Peres would not back any plots to oust Olmert from office, he recently told Kadima Knesset members. He would not, however, rule out being prime minister himself.
Peres stressed the government must be preserved and the ministers ought to concentrate on mending its flaws - and stop trying to oust Olmert.
Peres' adviser Yoram Dori said the vice premier was now busy stabilizing the government and correcting the malfunctions that the Winograd report addressed.
Senior Kadima sources said Saturday that the initiative to replace Olmert with Peres could gain momentum if it transpires that Olmert's survival efforts have failed, and if opponents of Foreign Minister Tzipi Livni in Kadima join the initiative. Livni's opponents, as well as people from Labor, Shas, Yisrael Beiteinu, will try to prevent her from being chosen as Olmert's replacement.
According to a report in Yedioth Ahronoth, Meretz MK Yossi Beilin met Peres last Thursday in an attempt to persuade him to replace Olmert and to prevent early elections.
Meanwhile, Olmert managed to stabilize his position within his party and the coalition, after the revolt against him failed; the only Kadima figures calling for his resignation are Livni, MK Avigdor Yitzhaki and MK Marina Solodkin.
Olmert said Saturday that he does not intend to fire Livni at this stage, but his aides continue to talk about her cowardice, subversiveness and lies. Olmert is maintaining Livni's dismissal as a future option.
Labor leadership contender former prime minister Ehud Barak on Saturday refrained from commenting on whether Labor should remain part of Ehud Olmert's government. Labor's central committee is to convene next week to discuss and vote on the issue.
Olmert and his associates are worried by the expanding momentum in Labor to quit the government before the party primaries on May 28, or if there is a second round in mid-June, as this may cause Olmert's coalition to topple.
Olmert is trying to bolster the coalition by obtaining the support of the ultra-Orthodox United Torah Judaism party.
A number of Labor MKs are expected to abstain in the no-confidence vote in the Knesset this week, or to absent themselves from the plenum.
Olmert's associates said that, in any case, the coalition has a very large majority.
Labor MKs Ophir Pines-Paz, Ami Ayalon, Dan Yatom and Eitan Cabel support quitting Olmert's government. MKs Shelly Yachimovitch and Avishai Braverman are expected to support the move as well.
Barak's associates say he will make his position known when the time is right. Unlike other candidates, Barak is in no hurry to issue statements and this is an indication of his experience, they say.
Barak is expected to try to prevent Labor from leaving the coalition, as this would plunge the political system into a tailspin of early elections, while Barak needs more time to rehabilitate his position to become an acceptable candidate for defense minister. He will therefore refrain from undertaking not to be part of Olmert's government.
National Infrastructures Minister Benjamin Ben-Eliezer told activists in the Arab community on Saturday "Labor's quitting the government means elections or a radical right-wing government headed by Benjamin Netanyahu."
"Labor must act responsibly and think a few steps ahead. Is this the alternative we want? To chain the feet of the new leader of our party? After all, we could always decide to quit ..." he said.
Defense Minister Amir Peretz, under pressure to resign over the scathing Second Lebanon War inquiry, said Saturday he intended to give up his post only after his Labor Party held its primaries on May 28.
"I announced more than a month ago that I intend, immediately after the Labor Party primaries, to carry out far-reaching changes," Peretz said on Channel 2 television.
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