Palestinians condemn move to build 700 new apartments in east Jerusalem settlements.
Tzipi Livni, the Kadima leader, said that Netanyahu’s offer was “cynical and unrealistic”.
She said that the offer was an attempt to use Israel’s international relations issues for “small-time politics”, adding such behaviour was “unworthy of the prime minister”.
Israel is under considerable pressure from the international community, particularly the US, to meet Palestinian pre-requisites for peace talks, such as the halting of settlement building in the occupied West Bank.
However, analysts have said that Netanyahu preferred to protect his coalition – currently comprising right-wing and religious parties – by not meeting those requests.
The centrist Kadima has 28 seats in the Knesset, the 120-seat Israeli parliament. That is one more than Netanyahu’s right-wing Likud party.
Netanyahu offered several cabinet posts without portfolios to Kadima politicians last week.
It has been suggested by experts that the move was an attempt to win the support of defectors, while splitting Kadima.
Livni earlier rejected an offer to join the ruling coalition after elections in March, disagreeing with Netanyahu’s hard line stance against the Palestinians.