Israel's Prime Minister Benjamin Netanyahu has asked centrist opposition leader and former foreign minister Tzipi Livni to join his government.

‘The prime minister asked Mrs Livni to join a national unity government ... in the face of the national and international challenges facing Israel today,’ a statement said.

Ms Livni's Kadima party, the largest in the 120-member parliament, has been rocked in recent days by reports that Netanyahu pressed several of its MPs to break away and join his coalition.

Ms Livni did not rule out the move.

‘If this is a serious offer, I have always said we can discuss the issue,’ an official in Livni's office quoted her as telling Netanyahu.

The premier told Ms Livni that a future unity government would be based on his vision of a Jewish state living alongside a Palestinian state which he outlined it in a major policy speech in June.

Netanyahu's right-wing Likud party currently leads a coalition that includes far-right and religious parties as well as the centre-left Labour party.

Following this year's March election, Ms Livni rejected a similar Mr Netanayhu offer to form a coalition together.