"I believe it's in Israel's interests and the Palestinian people's interest to have leaders willing to work toward the achievement of that state," Bush said at the White House with Palestinian President Mahmoud Abbas.
"People that can deliver that state, that vision, for the Palestinian people are sitting right here in the Oval Office - led by the president," Bush said.
Bush spoke as his own administration acknowledged that talks have bogged down five months after both sides pledged to reach a deal by January.
"I'm confident we can achieve the definition of a state," Bush said. "I'm also confident that it's going to require hard work."
Abbas headed into the meeting with the goal of prodding the Bush administration to pressure Israel to stop expanding Jewish settlements in the West Bank. A halt on those settlements - one of the most disputed aspects of the long-running Mideast conflict - is one condition of the map to peace for both sides.
Bush made no direct mention of the settlement issue in addressing reporters.
Abbas said Palestinian leaders are "doing everything we can" to reach a peace deal that would be satisfactory for his people and for Israel.
"I cannot say that the road to peace is paved with flowers," Abbas said. "It is paved with obstacles. But together, we will work very hard in order to eliminate those obstacles and achieve peace."
CBS News correspondent Mark Knoller reports the president -- calling Abbas a friend and a man of peace and vision -- said they would meet again next month when he's in the Middle East to attend the celebration of the 60th anniversary of the creation of Israel.