"To the extent that the federal government didn't fully do its job right, I take responsibility," Bush told a White House news conference on Tuesday at which he openly questioned US preparedness for another storm or a "severe attack".
Bush's rare admission of "serious problems in our response capability" came as the White House stepped up efforts to repair his public standing.
Bush will address the nation on Thursday from hard-hit Louisiana, his fourth visit to the disaster zone since Katrina struck.
White House spokesman Scott McClellan said Bush would use Thursday's address to "talk to the American people about the recovery and the way forward on the longer-term rebuilding".
The president's approval ratings have hit new lows, partly due to fierce criticism of the slow response to the 29 August hurricane, which killed hundreds and displaced one million people in the worst natural disaster in US history.
Some 54% of Americans disapprove of Bush's handling of the response, but 57% say state and local officials should bear responsibility for the problems, according to the latest Washington Post-ABC poll.
"To the extent that the federal government didn't fully do its job right, I take responsibility"
US President George Bush
Asked if Americans should worry that the government remains unprepared to respond to another major disaster or a terrorist attack, Bush said: "Katrina exposed serious problems in our response capability at all levels of government."
Bush himself raised questions about preparedness, after four years of record spending on domestic security since 11 September 11 2001.
"Are we capable of dealing with a severe attack or another severe storm? That's a very important question and it's in our national interest that we find out exactly what went on so we can better respond," he said at a news conference with Iraqi President Jalal Talabani.
Faced with sharp political and media criticism of the post-hurricane relief effort, Michael Brown resigned as head of the Federal Emergency Management Agency on Monday.
Republican senators with close ties to Bush have urged him to appoint a top official to lead the long-term recovery.
Hurricane Katrina displaced one
White House officials say that is among the options being discussed.
Former New York mayor Rudolph Giuliani, former secretary of state Colin Powell and retired General Tommy Franks, former head of the US Central Command, have been mentioned for the job.
Giuliani said on CNBC that a commission like the one that investigated the September 11 attacks could assess the response.
"Whether there were failures here on the state, city and federal level, I think a commission can decide that six months from now," he said. "No one person is responsible for this."