Exit polls show Kadima, the party founded by Ariel Sharon and led by Ehud Olmert, has won enough votes to lead a coalition government for the next four years.
The centrist group is projected to have between 29 and 32 seats, fewer than had been predicted.
In his speech, 60 year old Olmert first paid tribute to Sharon, who remains in a coma in a Jerusalem hospital after suffering a brain haemorrhage.
He then called for peace talks with Palestinian President Mahmoud Abbas, but made no mention of Hamas, the governing party.
He said that if the Palestinians were not willing or able then Israel would move forwards on its own.
Olmert wants to unilaterally draw Israel’s borders by 2010, dismantling outlying Jewish settlements in the West Bank while consolidating the larger ones inside the so-called security barrier.
Turnout for the election was at a record low of just over 63 per cent, the result some analysts say of a less than inspiring campaign and the fact that Sharon was absent.
The exit polls show the second largest party in Parliament will be Labour, with around 20 to 22 seats.
Leader Amir Peretz campaigned on social and economic issues.
A former trade unionist, he wants the minimum wage to be raised, and better provision made for the poor and disadvantaged.
His election to the head of Labour, ousting Shimon Peres, was one of the destabilising factors that led Sharon to call the election.
Labour said much of its competition came from GUIL the pensioners’ party led by Rafi Eitan.
It’s predicted to have made huge gains on previous results, taking 8 seats.