"President Abbas has been someone who has spoken out about ending the violence and stopping the terror, and we appreciate that. We want to continue to urge them to take steps in that direction," White House spokesman Scott McClellan said on Monday.
"We continue to urge the Palestinian leadership to take steps to put in place law and order in Gaza and move forward on good governance. We have been supporting them as they move forward on those efforts, and we will continue to do so," he said.
Bush was due to welcome Abbas to the White House on Thursday for talks expected to focus on efforts to crack down on resistance fighters and build up the Palestinian economy.
The meeting will come after Israel decided to suspend all contacts with the Palestinian Authority and impose restrictions on civilians in the West Bank following a shooting attack that left three Jewish settlers dead.
Following Israel's withdrawal from Gaza, the United States has
mostly put the burden for advancing the Middle East peace process on the Palestinians, prodding them to build up their security forces to quell anti-Israeli attacks.
State Department spokesman Sean McCormack urged the Palestinians to meet their obligations, "not only fighting to stop terror attacks but dismantle those terrorist networks that are responsible for these attacks".
"More needs to be done to stop these kinds of attacks," McCormack said.
"We are going to continue to work in close consultation with both sides to increase cooperation and contact between the two sides on security matters."