"President Abbas is a man devoted to peace and to his people's aspiration for a state of their own," Mr. Bush said. "And today, the Palestinian people are closer to realizing their aspirations."
At a news conference after a one-hour meeting in the Oval Office, Mr. Bush said "the way forward is confronting the threat armed gangs present to creation of a democratic Palestine."
Supporting Abbas, President Bush called on Israel to stop constructing settlements on the West Bank. He assured Abbas he shared his vision of two states living side by side in peace and security.
"Israel should not undertake any activity that contravenes its roadmap obligations," Mr. Bush said, referring to a blueprint for peacemaking approved by the United States, the United Nations, the European Union and Russia.
Without elaboration, the president said Israel would be "held to account" for any actions that hamper peacemaking or burden the lives of Palestinians.
But Mr. Bush said he was a "heck of a lot more confident" of peace prospects than when he first took office five years ago. Both Abbas and Israeli Prime minister Ariel Sharon are committed to making peace, he said.
Abbas, in response, insisted that Israel lift curbs on Palestinian travel in the West Bank, saying the restrictions had caused the Palestinians "hardship and humiliation."
The Palestinian leader also criticized Israel's security wall, particularly its location in Jerusalem, where the Palestinians intended to establish the capital of their state.
He assured Mr. Bush that election of a Palestinian legislature in January would establish one law to govern the area.