Citing unnamed administration officials, the newspaper said US Defense Secretary Donald Rumsfeld was reviewing the request.
Bremer's request underscores how difficult it has been for his small civilian staff and about 158,000 US-led troops to meet the demands of Iraqis for security and other basic needs, the Inquirer pointed out.
Since May 1, when Bush declared an end to major combat in Iraq, at least 26 American and six British soldiers have died as a result of hostile acts.
"It is a legitimate critique of this administration that we did a brilliant job of planning the war, we didn't do a brilliant job of planning what's going on now," the paper quotes one senior defense official as saying.
Senior US officials said Bremer had asked for dozens of civilian officials to make up for a shortage of skilled Iraqi administrators who were not closely affiliated with Saddam Hussein's regime, according to the report.
In addition, more US troops are needed as a "stopgap measure" until international peacekeepers start to arrive, The Inquirer quoted one official as saying.
A Defense Department spokesman declined to confirm or deny the report.