Israeli President Shimon Peres has formally invited foreign minister Tzipi Livni to form a new government.
The request followed the resignation on Sunday of Prime Minister Ehud Olmert, who faces several corruption inquiries.
Ms Livni, 50, last week replaced Mr Olmert as leader of Kadima, the largest party in the Israeli Knesset.
The former Mossad spy now has 42 days to form a coalition representing 61 seats in the 120-seat parliament.
If she is successful, she should be able to govern until elections in 2010.
But she said she would call an early election that if she failed to do so.
Mr Olmert denies any wrongdoing, but police have recommended he be indicted over two of the inquiries - accusations that he misused cash payments from a US businessman, and accusations that he double-billed government agencies for trips abroad.