Lieberman's backing significantly improves Netanyahu's chances of becoming prime minister.
However, Livni, the country's foreign minister, rejected the possibility of forming a coalition government and told a party meeting that Kadima must go into opposition.
"Today the foundations were laid for an extremist right-wing government ... there is nothing for us in such a government"
"Today the foundations were laid for an extremist right-wing government under the leadership of Netanyahu," she said.
"That is not our way and there is nothing for us in such a government ... we must be an alternative of hope and go into opposition."
Lieberman pledged his support to Netanyahu ahead of his planned meeting with Shimon Peres, Israel's president.
Peres has been meeting leaders of various political parties before deciding who to invite to form Israel's next government following last week's parliamentary elections.
The Israeli president has until February 25 to make his choice.
He began the task on Wednesday after receiving official results from February 10 general elections in which no party emerged with a clear majority.
Kadima came in first with 28 seats, Likud second with 27 and Yisrael Beitenu third with 15 seats.