President Bush, at an Army base that has seen 31 soldiers die in Iraq, sought Monday to reassure their families and an anxious nation that America is safer because of the mission there.

"All our military families that mourn can know this: Our nation will never forget the sacrifice that their loved one made to protect us all," Bush said. "By the unselfish dedication of Americans in uniform, children in our own country and in lands far away will be able to live in freedom and know the peace that freedom brings."

Bush's message of resolve on Iraq (search) -- delivered twice Monday, in twin speeches at the Defense Department headquarters in Washington and before about 5,000 people crowded inside a hangar here at the base of the Rocky Mountains (search) -- came a day after two U.S. soldiers were slain in Mosul, previously one of the safest areas of Iraq for coalition forces. Also Sunday, a soldier traveling in a convoy was killed by a roadside bomb and five Americans were killed when a transport helicopter crashed in Afghanistan.

The deaths -- especially those in Mosul (search) -- underscored the worries about Iraq that are beginning to show up in polls and pose a potential re-election hazard to the president. After months in which more than half of Americans approved of the president's handling of Iraq, a recent CNN-USA Today-Gallup poll showed disapproval at 54 percent and approval at 45 percent. Other polls find the public evenly divided.

Those concerns were reflected Monday even among people at Fort Carson, which has sent 12,000 troops to Iraq and been deeply affected by a death toll that base officials adjusted upward twice just on Monday.

The 31 lost included a newlywed due to come home for a visit at the end of the week, as well as three fallen National Guard soldiers. They also included four who were killed earlier this month when a helicopter was shot down near Fallujah.

"My only problem with the administration and the country's campaign in Iraq is they could have done a better job of explaining why we're over there," said 1st Lt. Ted Stutz.

"What makes me mad the most is past presidents have gone to funerals and he hasn't gone to any," Lori Hartman, whose husband, Spc. Corey Hartman, is heading for Iraq in February. "It's like he wants to turn his back and not realize what's really going on."

Seeking to contradict such impressions, Bush spent more of his time on the base interacting personally with soldiers and family members than delivering his public address.

A White House official said the president spent about an hour and 40 minutes with about 100 relatives of killed and wounded soldiers from Fort Carson, spread among four rooms. The official, speaking on condition of anonymity, described it as a very emotional meeting and quoted one father whose son had died in Iraq as telling Bush, "He died for freedom."

Bush's first stop was lunch with about 170 camouflage-clad Fort Carson personnel, where he chose fried chicken and corn on the cob from a mess hall cafeteria line. Later, he met privately for almost two hours with nearly 100 relatives, representing 26 of the killed Fort Carson soldiers.

"These are challenging times for military families," he said in his speech. "I want to thank the families of the fallen soldiers who are here with us today. Our prayers are with you. We ask for God's strength and God's guidance."

Melissa Givens, whose husband, Pfc. Jesse Givens, was the first Fort Carson soldier to die in Iraq, appreciated Bush's effort.

"My husband believed in what he was doing and believed in our president. I feel the same way," she said.

The president promised that the United States' "resolve will not be shaken" in the global war against terrorists. The war in Iraq, he argued, is crucial to that effort -- and will be successful.

"Because we're fighting terrorist enemies thousands of miles away in the heart and center of their power, we are making the United States of America more secure," said Bush, who wore an olive green Army jacket over his shirt and tie and was greeted enthusiastically.

He also defended his administration's newly toughened strategy for combatting insurgents in Iraq, despite nearly daily upticks in the death toll.

"We're sending a clear message: Anyone who seeks to harm our soldiers can know that our great soldiers are hunting for them," he said.

Earlier, Bush signed into law a $401.3 billion bill authorizing 2004 defense programs that gives the department greater control over its civilian work force and eases environmental restrictions on the military. It also provides new benefits to active duty soldiers and veterans.

The bill does not provide the money for military programs, most of which comes from a $368 billion appropriations bill signed by Bush in September.

"America's military is standing between our country and grave danger," he said at the Pentagon ceremony.

The president traveled to Colorado en route to a weeklong stay at his Texas ranch for Thanksgiving. On Tuesday, he makes a day trip to Las Vegas for a campaign fund-raiser and a speech on Medicare, followed by similar appearances in Phoenix.