"Our hope is that president Abbas and the prime minister (Salam) Fayyad will be strengthened to the point where they can lead the Palestinians in a different direction with a different hope," said Bush.

Abbas on Sunday expelled Hamas from the Palestinian unity government and appointed an emergency cabinet after the radical Islamists seized full control of the Gaza Strip in bloody battles which left over 110 people dead.

Ahead of two hours of one-on-one talks, Bush and Olmert sought to bolster Abbas's position, whose move has encountered some Palestinian criticism, with both leaders affirming "he is the president of all the Palestinian people."

"I want to strengthen the moderates and cooperate with president Abbas," said Olmert, who met Bush for the third time in just over a year.

The two leaders said the new cabinet was a chance for renewing the stalled talks between Israel and the Palestinians based on Bush's 2002 vision for a two-state solution to Middle East peace.

"We share a common vision of two states living side-by-side in peace," Bush said at the White House. He nevertheless refused to set out a clear timeframe for the creation of a Palestinian state.

His proposals for two states based on the internationally-backed "road map" to peace have failed to materialize since talks broke down in 2000.

"I am going to make every possible effort to move forward to see how things can be worked jointly, in order to provide Palestinians a real, genuine chance for a state of their own," added Olmert.