Retired Army Major Gen. John Riggs told National Public Radio that Rumsfeld fostered an "atmosphere of arrogance." And retired Major Gen. Charles Swannack told CNN that Rumsfeld micromanaged the war. "We need a new secretary of defense," he said.
Last month, Army Major Gen. Paul Eaton wrote in the New York Times that Rumsfeld was "incompetent strategically, operationally and tactically."
While Rumsfeld has offered his resignation at least twice to President Bush in the past, he has not talked to the White House about resigning in the face of this current criticism and is not considering it, reports CBS News White House correspondent Jim Axelrod.
The White House insists Rumsfeld retains President Bush's confidence. Few close to the administration expect him to be shown the door.
"The president believes Secretary Rumsfeld is doing a very fine job during a challenging period in our nation's history," Bush spokesman Scott McClellan said Thursday as the administration circled its wagons around the embattled Pentagon chief.
Military experts say the parade of recently retired military brass calling for Rumsfeld's resignation is troubling and threatens to undermine strong support Bush has enjoyed among the officer corps and troops.
With public anti-war sentiment increasing, "the president and his team cannot afford to lose that support," said Kurt Campbell, a former deputy assistant secretary of defense.
Yet for Mr. Bush to try to distance himself from Rumsfeld "would call into question everything about the last three years' strategy in ways the White House worries would send a very negative message," said Campbell, now with the Center for Strategic and International Studies.
Joining the criticism earlier this week was retired Army Maj. Gen. John Batiste, who served as an infantry division commander in Iraq until last November. He called for a "fresh start at the Pentagon," accusing Rumsfeld of ignoring sound military decision-making and seeking to intimidate those in uniform.
Earlier calls this year for Rumsfeld's replacement came from retired Marine Gen. Anthony Zinni and retired Marine Lt. Gen. Gregory Newbold.
The most nettlesome member of Mr. Bush's Cabinet, Rumsfeld has been a lightning rod since the war began in March 2003.
He was blamed for committing too few U.S. troops and for underestimating the strength of the insurgency. He took heat in 2004 over the abuse of Iraqi prisoners at the U.S. Army-run Abu Ghraib prison, and for a brusque response he gave to an Army National Guard soldier in Kuwait who questioned him on inadequate armor.
Republicans in Congress have offered Rumsfeld little in the way of public support.
As to the latest general to call for Rumsfeld's resignation, "I don't know how many generals there are. There are a couple thousand at least, and they're going to have opinions," Pentagon spokesman Eric Ruff said Thursday. "It's not surprising, we're in a war."
But it is surprising, especially because it's a time of war, said P.J. Crowley, a retired Air Force colonel who served as a Pentagon spokesman in both Republican and Democratic administrations and was a national security aide to former President Clinton.
"This is a very significant vote of no confidence and I think the president has to take this into account. The military is saying it does not trust its civilian leadership," said Crowley, now a senior fellow at the liberal Center for American Progress.
Rumsfeld himself answered "no" when asked this week whether the march of retired generals was hurting his ability to do his job. "There's nothing wrong with people having opinions," he said.
Gen. Peter Pace, chairman of the Joint Chiefs of Staff, has become Rumsfeld's strongest defender in uniform. "He does his homework. He works weekends, he works nights. People can question my judgment or his judgment, but they should never question the dedication, the patriotism and the work ethic of Secretary Rumsfeld," Pace said.
Mr. Clinton, a Vietnam war protester who avoided the draft, was mistrusted by many in the military, and some top-ranking officers publicly questioned his policies in congressional testimony. But Mr. Bush, a pilot in the Texas Air National Guard during the Vietnam era, has counted on strong support on military bases, one of his favorite destinations.
Mr. Bush's dilemma, said Michael O'Hanlon, a military analyst with the Brookings Institution, is that he "shares a lot of the responsibility for the key decisions on Iraq."
"Bush is implicated. For Bush to fire Rumsfeld is for Bush to declare himself a failure as president. Iraq is the main issue of his presidency," said O'Hanlon, who supported President Bush's decision to invade Iraq and said he still supports the war.