Right-wing leader Benjamin Netanyahu has accepted a mandate to form Israel's next government.
President Shimon Peres nominated Mr Netanyahu on Friday, making clear he had done so because the Likud party leader could command a clearer majority in parliament.
Mr Netanyahu, 59, was prime minister before in the late 1990s and now has six weeks to put together a coalition for a second turn at the helm.
Likud more than doubled its seats in the election on 10 February in which the security of the Jewish state was the paramount issue, after a 2006 conflict with Hezbollah Islamists in Lebanon and a war with Islamist Palestinian Hamas in Gaza last month.
However there was no clear winner. The centrist Kadima party won 28 of 120 seats compared to 27 for Mr Netanyahu's Likud.
Mr Netanyahu called for a broad, national unity coalition with centrist and left-wing partners, but there was little sign they would accept.
The leader of the centrist Kadima party, Tzipi Livni, has indicated she is not interested. She had herself sought the premiership nomination from President Shimon Peres, citing the unbroken tradition of the leader of the largest party being invited to form a government.
Mr Netanyahu's rivals to the left favour pursuing talks with secular Palestinian leaders, backed by US President Barack Obama, that could hand most of the occupied West Bank and parts of Jerusalem to a new Palestinian state in return for peace.
If his rivals do not agree on a coalition Mr Netanyahu may have no alternative but an alliance with far-right and ultra-religious parties, which could tie his hands on making peace with the Palestinians.
