Israel President Reuven Rivlin has called on Benjamin Netanyahu and Isaac Herzog to work together to form a national unity government, but it does not seem likely they will join together in the same cabinet.
Mr Netanyahu repeatedly said throughout the election campaign that he would not sit in government with Mr Herzog and his partner in the Zionist Union leadership, Tzipi Livni.
For now, Mr Netanyahu is already talking with Likud's "natural partners" about forming a coalition. Next week all the parties' leaders will meet President Rivlin to recommend a candidate for the premiership, but this is now little more than a formality - there is only one candidate.
The coalition which will form the base for the fourth Netanyahu government includes Bayit Yehudi - whose leader, Naftali Bennett, was the second person Mr Netanyahu called on election night - Shas, Yisrael Beiteinu and United Torah Judaism.
Together with Likud, these religious and right-wing parties have 57 seats. To complete his majority, he will also need Kulanu, the new centrist party headed by former Likud minister Moshe Kahlon.
Mr Kahlon was expected to drive a hard bargain with either candidate, but now that only Mr Netanyahu remains in the running, his position is considerably weaker.
But there are many in Likud who believe that Mr Netanyahu will try to seek an agreement with the man who until Tuesday night was his rival.
Bringing Labour into the government could serve him in a number of ways. It would create a broader-based and therefore more stable coalition, in which none of the parties could topple the government by leaving.
It would lower the demands of each coalition partner and also limit the influence of some of the members of Mr Netanyahu's own party. That is something he would welcome.
As Israel is expected to face increased international pressure over the Palestinian issue, having both Herzog and Livni in his cabinet will allow the prime minister to project a more moderate image to the world.
In such a case, Mr Herzog could serve as foreign minister, a radical change to the incumbent Avigdor Leiberman, who with only six seats in the new Knesset will not receive a major portfolio in the government.
The prospect of such a government still seems remote. The supporters at the Likud victory-rally night made their feelings clear, chanting "we don't want unity" as Mr Netanyahu mounted the podium.
As the newly-elected PM, he can face down any internal opposition - but can Mr Herzog? Even if he decides he prefers to serve within the government and gain the experience and recognition of a senior ministerial role, he will have a tough time selling it within Labour.
For now it isn't even an option, but as the new coalition begins to take shape over the coming weeks there will be added pressure on the Labour leader to abandon his opposition pledge and do what he can to prevent the formation of a solely right-wing government.