The normally stoic Rumsfeld said when he meets wounded soldiers or relatives of those killed in battle, "their grief is something I feel to my core."
"I am truly saddened by the thought that anyone could have the impression that I, or others here, are doing anything other than working urgently to see that the lives of the fighting men and women are protected and are cared for in every way humanly possible," he said.
"And I hope and pray that every family member of those who have died so bravely knows how deeply I feel their loss."
Rumsfeld has been a lightning rod since the war began in March 2003, but criticism recently intensified after a Tennessee National Guardsman in Kuwait asked him during a question-and-answer session with soldiers on Dec. 8 why he and his comrades had to scrounge for armor to protect their vehicles.
Rumsfeld gave an extended answer that included the statement, "You go to war with the Army you have, not the Army you might want or wish to have."
Critics called the response insensitive and castigated him for not doing more to prepare the U.S. military for the Iraqi invasion and its aftermath.
The following week, some Republicans joined Democrats in voicing dissatisfaction with Rumsfeld.
Sen. John McCain, R-Ariz., said he had "no confidence" in Rumsfeld, citing the defense secretary's handling of the war and the failure to send more troops. Sen. Trent Lott, R-Miss., said he believes Rumsfeld should be gone within a year. Neither directly called for his resignation.
The defense secretary was criticized again last weekend when it was reported that he did not personally sign letters of condolence to the families of dead soldiers, but instead relied on a mechanical device to affix his signature. He immediately abandoned the practice.
"My goodness, that's the least that we could expect of the secretary of defense, is having some personal attention paid by him," Sen. Chuck Hagel, R-Neb., said Sunday.
The next day, President Bush defended Rumsfeld, who has agreed to stay on for Bush's second term, saying his defense secretary was "doing a very fine job."
A CNN-USA Today-Gallup poll released Monday found 52 percent of respondents believe Rumsfeld should resign, and 41 percent approve of his job performance. People were evenly split on Rumsfeld's performance in May, but most approved of his handling of the job about a year ago.
On Wednesday, Rumsfeld said, "I, and I know others, stay awake at night for concern for those at risk, with hope for their lives, for their success. And I want those who matter most, the men and women in uniform and their families, to know that. And I want them to know that we consider them, the soldiers, the sailors, the airmen, the Marines, to be America's true treasure. And I thank them and I thank their families."
Asked whether the criticism had undermined his ability to do his job, he said, "You get up in the morning and you think about what our troops are doing. And I must say, if they can do what they're doing, I can do what I'm doing."