Mr Mofaz made a call for party unity soon after the result was announced.
He said: "From tonight, the path to unseating Netanyahu has begun. From tonight, there is one Kadima. A united and strong Kadima will return Israel to the right path."
He pledged to expand the numbers of Charedim serving in the Israeli army and to further social progress in Israel.
Ms Livni, who has been a star of the party since it was formed by former Prime Minister Ariel Sharon in 2005, would not reveal whether her defeat would mean her departure from Kadima. She said she had wished Mr Mofaz good luck and accepted the results.
Ms Livni briefly served as the Israeli prime minister after Ehud Olmert stepped down amid corruption allegations, but although the party won more seats than Likud in the Februyary 2009 election, she was unable to form a coalition.
