If finalized, the agreement, reached late Sunday, could make Mr. Lieberman, an often indelicate and outspoken politician whose threatening language aimed at Arabs arouses suspicion and some trepidation abroad, the next foreign minister.
The attention of many Israelis was focused on Cairo, however, where Israeli negotiators were trying Monday to reach a deal with Hamas, the militant group that governs Gaza, for the release of a captured Israeli soldier, Cpl. Gilad Shalit.
The latest attempt appeared to have failed. In a statement issued Monday night, the office of the departing Israeli prime minister, Ehud Olmert, said that Hamas had hardened its position during the talks and raised extreme demands, despite what were described as generous proposals from Israel.
Hamas demands the release of hundreds of imprisoned Palestinians, including many convicted of deadly terrorist attacks, in exchange for Corporal Shalit, who was captured by Palestinian militants and taken into Gaza in 2006. A senior Hamas official, Moussa Abu Marzouk, suggested that there had been progress in the talks and that his group was awaiting a positive Israeli response to its demands.
The Israeli negotiators, dealing indirectly with Hamas through Egyptian mediators, were hoping to reach an agreement before Mr. Olmert ended his term. Mr. Olmert called a special cabinet meeting for Tuesday to brief ministers on the talks.
The family of the captured soldier has expressed concern about leaving his fate in the hands of the incoming government, fearing that it might start studying the case from scratch. A rightist government may also take a harder line in any further negotiation.
The Likud and Yisrael Beitenu parties have expressed a preference for a broader unity coalition that would include the centrist Kadima Party, which is led by the departing foreign minister, Tzipi Livni. Yisrael Beitenu has agreed to make changes in its coalition agreement should Kadima join, and in that case, the job of foreign minister would probably be reassigned.
Dina Libster, a Likud spokeswoman, said Monday that there was “still hope” that Kadima would join.
But the Likud, she said, was close to signing another coalition agreement with the rightist, ultra-Orthodox Shas Party, to be followed by smaller right-wing and religious parties, to give Mr. Netanyahu a majority in the 120-seat Parliament. It seemed increasingly unlikely that Ms. Livni, a strong advocate of negotiations with the Palestinians for a two-state solution, would cooperate at this stage.
Kadima narrowly beat the Likud in the Feb. 10 parliamentary elections but the showing of right-wing parties led President Shimon Peres to pick Mr. Netanyahu to try to form a governing coalition. Mr. Netanyahu has so far resisted Ms. Livni’s demands for a clear commitment to the two-state solution and full power-sharing to the point of a rotating premiership in return for Kadima’s participation in the next government.
In addition to the Foreign Ministry, Mr. Netanyahu’s agreement with Yisrael Beitenu also assigns Mr. Lieberman’s party the Tourism, National Infrastructure, Immigrant Absorption and National Security Ministries.
Mr. Lieberman ran a contentious election campaign that many here and abroad saw as racist, focusing on the question of loyalty of the Arab citizens of Israel, who make up about a fifth of the population. Yisrael Beitenu proposed an oath of loyalty to the state that would be taken by all citizens, but that was mainly directed at the Arab minority.
Gadi Wolfsfeld, a professor of political science at the Hebrew University of Jerusalem, said he had been “incensed” by the campaign and how lightly it was taken by so many Israelis. That Yisrael Beitenu won 15 seats, he said, did not make the party “any less extreme.”
Mr. Lieberman’s positions are sometimes contradictory and hard to fathom. A West Bank settler, he advocates the creation of a viable Palestinian state. Yet he withdrew his party from Mr. Olmert’s governing coalition more than a year ago in anger over the resumption of Israeli-Palestinian peace talks.
In the coalition agreement with the Likud, there is no mention of a peace process or peace talks.
Nor is there any mention of a loyalty oath, though the agreement states that the new government will deal with disloyalty and will amend the citizenship law, for example, to strip Israelis of citizenship if they are convicted of spying.
Irena Etinger, a spokeswoman for Yisrael Beitenu, said that this was “the first step” and that others would follow.
In a commentary published in The Jewish Week in New York late last month, Mr. Lieberman said he looked forward to working with President Obama in the next government. “I know that U.S.-Israel relations are as strong as ever,” he said, “and that our shared values and interests make our friendship unshakable.”