The revelations about Mr. Bush's criticism, which according to The New York Times were made with the president's knowledge, were a rare admission of discord from this White House, reports CBS News Correspondent Bill Plante.
The prison controversy erupted last week whenaired photos depicting apparent abuse. The photos showed prisoners hooded and nude, forced into sexual positions and piled together. One was attached to wires and was allegedly told that he might be electrocuted.
The Army has acknowledged that at least a dozen deaths at prisons and detention camps remain under scrutiny by criminal investigators. The CIA is reviewing at least two additional deaths.
The Los Angeles Times reports the CIA is also probing whether its agents were involved in creating so-called "ghost detainees," who were imprisoned without documentation and possibly hidden from Red Cross officials.
The Times reports Mr. Bush was upset that Rumsfeld had not told him about the photographs before they were broadcast.
"The president was not satisfied or happy about the way he was informed about the pictures, and he did talk to Secretary Rumsfeld about it," an official told The Times.
Rumsfeld himself did not know about the images of naked prisoners and gloating U.S. soldiers until the broadcast, a senior White House official said.
In interviews on Arab television Wednesday, Mr. Bush said he retained confidence in Rumsfeld.
Rumsfeld was summoned by angry lawmakers to testify on Capitol Hill on Friday, while senators — Republicans and Democrats alike — discussed a resolution to condemn the abuses.
"I don't presume to tell the president what he should do," Sen. John McCain, R-Ariz., told the CBS News Early Show. "But it's obvious that there's a lot of explaining that Secretary Rumsfeld and others have to do, including why congress was never informed as to this. "
Like other senators, McCain complains that Rumsfeld did not mention the impending abuse story when he briefed them on Capitol Hill the day of the broadcast.
"I think that's what's sparked a lot of outrage here," McCain said. "And I think there's going to be repercussions about that, because we do have a responsibility here in Congress."
On Thursday, a newspaper said it had obtained more pictures possibly depicting abuse at the Abu Ghraib prison, and the international Red Cross said it had repeatedly asked U.S. authorities to take action over prisoner abuse and that American officials reacted positively before recent revelations about the way detainees were treated.
"The American authorities took very seriously all our recommendations," said Nada Doumani, spokeswoman for the International Committee of the Red Cross, speaking from Amman, Jordan.
The ICRC, which visits prisoners held by coalition authorities in Iraq, had previously refused to comment publicly on conditions at the prison or say whether it had discussed allegations of prisoner abuse with U.S. officials.
ICRC officials noted that the United States had been taking steps against some of the people allegedly involved in the abuses of prisoners.
The Washington Post, in its Thursday editions, said it had obtained a new batch of more than 1,000 digital photos from Iraq. The newspaper said the photos ranged from snapshots depicting everyday military life to graphic images of what appeared to be a female soldier holding a leash that goes around a naked man's neck at Abu Ghraib prison. Friends and relatives of the soldier with the leash said the photo must have been staged, the Post said.
In an, Mr. Bush said on Wednesday that Americans were appalled by the abuse and deaths of Iraqi prisoners at the hands of U.S. soldiers. He promised that "justice will be delivered."
"The people in the Middle East must understand that this was horrible," Mr. Bush said. He appeared on two Arabic-language television networks to take control of the administration's damage-control efforts.
While Mr. Bush did not offer an apology, Condoleezza Rice, his national security adviser, had said Tuesday that, "we are deeply sorry for what has happened."
In Iraq, the new general in charge of prisons there apologized for the mistreatment of detainees at Abu Ghraib prison, and troops launched a new offensive against the followers of a rebel cleric.
"These are violations not only of our national policy but of how we conduct ourselves as members of the international community," Maj. Gen. Geoffrey Miller said.
According to anat Abu Ghraib, Miller conducted a review of U.S.-run prisons in Iraq last fall. In it, Miller said prison guards should create conditions favorable for interrogations. The Army investigation found that guards at Abu Ghraib were doing so.
Reaction in the region to Mr. Bush's remarks was generally skeptical.
"Bush's statements today will not restore the dignity which the tortured detainees lost," said Sari Mouwaffaq, a Baghdad mechanic.
But Raad Youssef, a 49-year-old teacher in Baghdad, said that during Saddam's rule, "there were many genocides that were committed and nobody dared to reveal them at that time and now officials of the former regime did not try to apologize. Bush's attempt to repair the damage is a good thing in my opinion."
Sen. John Kerry, Mr. Bush's Democratic rival, said the president's remarks Wednesday were not enough.
"The president of the United States needs to offer the world an explanation and needs to take appropriate responsibility," Kerry said. "And if that includes apologizing for the behavior of those soldiers and what happened, they ought to do that."
McCain told the Early Show that Abu Ghraib prison, a symbol of torture in the Saddam era, should be razed. He also said U.S. military detention policies outside Iraq must be reviewed, and prisoners at Guantanamo Bay put on trial or released.