Atta and al-Shehhi were on two of the hijacked planes
Mr Ashcroft said that the review should include not only the INS's failure to stop the delivery of the notification letters, but also the source of the delay in processing the letters.
President George W Bush said he was "stunned" by the incident. Earlier the White House said he had ordered US Director for Homeland Security Tom Ridge to work with Mr Ashcroft to prevent this from happening again.
Call for reform
"The INS needs to be reformed and we've got to push hard to do so... It needs to be modernised so we know who's coming, and who's going out and why they're here," Mr Bush said.
"This is inexcusable, this an interesting wake-up call for the people that run the INS," he added.
Mr Ashcroft issued a memorandum requesting the Justice Department's Inspector General to conduct a thorough investigation.
"It is inexcusable when document mismanagement leads to a breakdown of this magnitude," Mr Ashcroft said.
"Individuals will be held responsible for any professional incompetence that led to this failure, and inferior INS quality-control mechanisms will be reformed," he added.
Visa status changed
The INS admitted on Tuesday that the two hijackers, Mohammed Atta and Marwan al-Shehhi, had had their visas changed from visitor to student.
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.
Lack of information
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.
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.