He designated Friday of next week as a national day of prayer and remembrance for victims across the Gulf Coast.
Bush spoke as Congress rushed to approve $51.8 billion in emergency relief and recovery aid for hurricane victims. Under fire for the government's slow response, Bush said his remarks were intended specifically for the tens of thousands of people forced from their homes by the hurricane.
On Capitol Hill, Democratic leaders said they intended to boycott a proposed Republican-led congressional committee that is to investigate the administration's readiness and response to the storm.
"I do not believe that the committee proposed by Speaker Hastert and Senator Frist is in the best interest of the American people," said Sen. Harry Reid, D-Nev. Both he and House Democratic Leader Nancy Pelosi said they would not appoint members to the panel as currently contemplated.
Bush said he recognized that many displaced people lacked proper identification or even a change of clothes, and said the government would "cut through the red tape" to ensure that they receive the help they need. He encouraged evacuees to register with the Federal Emergency Management Agency to receive the immediate $2,000 in assistance and then longer term aid.
"We have much more work to do," the president said. "But the people that have been hurt by this storm know that - need to know that the government is going to be with you for the long haul."
Bush said that more than 400,000 families have registered with FEMA but tens of thousands more people still need to be processed.
"The responsibility of caring for hundreds of thousands of citizens who no longer have homes is going to place many demands on our nation," the president said. "We have many difficult days ahead, especially as we recover those who did not survive the storm."
Bush said the government also would relax requirements so that evacuees relocated far from home could receive state-administered federal benefits, such as Medicaid, welfare, child care, mental health and substance abuse treatment, food stamps, housing, foster care, nutrition for poor, pregnant women, school lunch and unemployment checks. He said states that are housing evacuees should "not be penalized for showing compassion" - meaning the government would reimburse them.