Atta and al-Shehhi were on two of the hijacked planes
"He [Bush] wants to know how and why this happened, and he wants it fixed," said White House spokesman Scott McClellan.
Mr McClellan added that Mr Bush had ordered US Director for Homeland Security Tom Ridge to work with US Attorney General John Ashcroft in order to prevent this from happening again.
The US flight school where two of the 11 September hijackers trained received letters saying their visa applications have been approved - six months after the World Trade Center attacks.
The INS admitted on Tuesday that the two hijackers, Mohammed Atta and Marwan al-Shehhi, had had their visas changed from visitor to student.
Approvals
The INS approved the men's application to stay in the country on 17 July.
The INS said the Huffman International Flying School was informed about the decision last summer and the latest documents were "back-up notification" which had been delayed in being sent out.
Atta, who came from Egypt, and al-Shehhi, of the United Arab Emirates, trained at the flying school in July, last year.
They had entered the United States on visitors' visas and applied for M-1 visas, given to students on technical courses.
The INS then gave its approval for Atta and al-Shehhi to remain in the US until 1 October, 2001, the Associated Press news agency reported.
Backlog of paperwork
A spokesman for the INS blamed a backlog of paperwork at a processing centre in Kentucky for the delay in dispatching the letters.
"The important thing to recognise is the decisions to change their status were made... before 11 September, and at the time there was no information made available to INS regarding these people," said Russ Bergeron.
The owner of the flight school, Rudi Dekkers, said Atta and al-Shehhi had applied for the visas on 29 August, 2000, before they began their six-month training course.
US authorities believe Atta, who was 33, was the ringleader of the group which hijacked four planes on 11 September.
He was one of four hijackers who seized American Airlines Flight 11 from Boston to Los Angeles and flew it into the north tower of the World Trade Center.
Al-Shehhi is believed to have piloted United Airlines Flight 75, also from Boston to Los Angeles, which ploughed into the south tower 17 minutes later.