In an interview on NBC Television broadcast on Sunday night, Bremer said he sent a memo to Donald Rumsfeld, the defence Secretary, suggesting that half a million soldiers would be needed, three times the number deployed by the Bush administration in Iraq.
"I never had any reaction from him," Bremer told Brian Williams, an interviewer on Dateline.
Although he never heard back from his direct boss, Bremer said he did discuss his concerns with George W Bush.
Quoting Bremer, the network said President Bush replied that he would try to get more troops from other countries "but made no mention of increasing the number of American forces".
Bremer thought the Pentagon painted a false picture of the capability of the Iraqi force, which would take over when the Americans departed.
"I raised my concerns about the numbers and quality of these [Iraqi] forces - really right from the beginning," he said.
Asked why he did not go public with his concerns, Bremer defended what he considered his obligation to "tell the president what you think ... in private, through the appropriate channels, as I tried to do".
No military strategy
Bremer, who is trying to promote his book on Iraq, acknowledged that in November 2003 he told Dick Cheney, the vice-president, that he was worried that there was no military strategy for Iraq and that the policy was driven more by the Pentagon's plan to bring troops home by the spring of 2004.
The book, "My Year in Iraq: The Struggle to Build a Future of Hope", is due to be released on Monday.
"He [Cheney] thought there was something to be said for the argument that we didn't have a strategy for victory at that time"
Paul Bremer, leader of the US civilian occupation authority in Iraq after the 2003 invasion
"The vice-president said to me, 'Well, I have similar concerns'," Bremer said in the interview.
"He thought there was something to be said for the argument that we didn't have a strategy for victory at that time."
Publicly, Cheney, a major cheerleader of the administration and its war efforts, has not hinted at such misgivings.
There was no immediate comment from Cheney, Rumsfeld or the White House on the latest Bremer revelations.
Disbanding the Iraqi army
Bremer spoke about the decision to disband the Iraqi army quickly after arriving in Baghdad, which many experts say was a serious miscalculation.
He said it was not fair to fault him for the decision because "it wasn't me" who made it and because the Iraqi army had largely disintegrated on its own in the face of the US invasion.
Bremer said the decision to
disband the Iraqi army was not his
"The decision was discussed by my advisors with the seniors civilians in the Pentagon for weeks before I made my recommendation, which was approved in Washington," he said.
Despite his criticisms, Bremer said he still supported the war in Iraq. "We've got young Americans dying over there still today," he said. "That is a painful price of war. That doesn't make it wrong. It just makes it difficult."
The comments by Bremer, who during his tenure as Iraq's ruling administrator defended US policy, could fan a new wave of criticism.