Men armed with tools and hardhats returned to work Tuesday moring amid the rubble of the collapsed World Trade Center, moments after commemorating the three-month anniversary of the attacks that killed thousands of people and left a legacy of pain and destruction in their wake.

Bagpipes mourned the dead under the drizzling rain at Ground Zero where more remains of victims were pulled out of the debris on Monday. Meanwhile, the National Anthem was sung by a New York City Police officer at the New York Stock Exchange, which had been hit particularly hard by the Sept.11 attacks.

And in Washington D.C., the President clutched a hand to his heart as the National Anthem played in the East Room of White House. Members of  his cabinet called attention to the victims of the third hijacked plane, which slammed into the side of the Pentagon killing 125 on the ground and 64 on the plane.

A similar ceremony recalled the victims of the fourth hijacked plane, which crashed in rural Pennsylvania.

"We remember the children traveling without their mothers when the planes were highjacked. We remember the cruelty of the murderers and the pain and anguish of the murdered," Bush said. "Everyone of the innocents who died on Sept. 11 was the most important person on earth to somebody."

Defense Secretary Donald Rumsfeld, speaking at the Pentagon memorial, said the U.S. fighting forces in Afghanistan are there to ensure the freedom of the living from those who show no respect for the concept.

"Our fighting forces are teaching the al Qaeda forces a lesson, a lesson not taught on the camps that train them to murder and to terrorize," he said. "They are teaching them ... no weapon in any arsenal is as formidable as the will and the moral courage of free men and free women." 

Bush had encouraged the nations of the world to join in the commemoration Tuesday, reminding them that citizens of more than 80 countries died in the attacks.

He said America does not need monuments and memorials to grieve the deaths of more than 3,000 people in suicide hijackings over New York, Washington and Pennsylvania. 

"For those of us who lived through these events, the only marker we'll ever need is the tick of a clock on the 46th minute on the 8th hour of the 11th day," the president said. "We'll remember where we were and how we felt. We'll remember the dead and what we owe them. We'll remember what we lost and what we found." 

Solicitor General Ted Olson, whose wife, Barbara, died in the hijacked plane that crashed into the Pentagon, spoke at a Justice Department ceremony. 

"We will never forget our loved ones who died or who were wounded on Sept. 11," Olson said. "We will fight this evil for as long and as patiently as it takes. We will prevail. We will comfort and care for those who have suffered. We will not forget." 

At Ground Zero, prayers were offered by Christian, Muslim and Jewish clergy. "They took down those structures, but they will not take away the spirit," said Rabbi Joseph Potasnik, a Fire Department chaplain. 

"We pray for all the families — the husbands, the wives, the children, the mothers," said John Hiemstra, director of the Council of Churches of NYC. "The geographical, cultural and religious walls that may have divided us have been bridged." 

At the Department of Transportation Washington several hundred employees gathered in the courtyard for a small ceremony in memory of the victims. 

"The cowardly terrorist attacks require all of us to work harder than ever before," Transportation Secretary Norman Mineta told the group. 

After Coast Guard Captain Leroy Gilbert delivered a prayer the audience stood in silence until the Coast Guard band played the national anthem. 

From New York's ground zero to the Pentagon to the Ukraine, commemorations began at the same moment. More than 70 countries held simple ceremonies, from Great Britain and Japan to South Korea and Denmark. In New Delhi, India, U.S. Ambassador Robert Blackwill said the world "will forever be marked" by the attacks, and in Australia, diplomats planted a symbol of life -- an oak sapling.

Later, Bush was to visit the Citadel, the state military college in Charleston, S.C. He was to outline his views on the new demands the war on terrorism is placing on the military and on intelligence-gathering, and offer a vision of how the new coalition could change the global landscape. 

The Citadel was the site of a speech Bush gave during his presidential campaign in September 1999, and aides distributed that text, eager to point out that Bush seemed to sense the danger of terrorism. 

In that speech, Bush warned of "an era of car bombers and plutonium merchants and cyberterrorists and drug cartels and unbalanced dictators." 

"Once a strategic afterthought, homeland defense has become an urgent duty," he said then. 

Tuesday's speech was also to cover the United States' thawing relationship with Russia, bioterrorism and what Bush sees as the potential for a new world order, improving long-tense relationships with such nations as Pakistan, India and Russia in the anti-terror campaign. 

Mostly, though, Bush was to focus on transforming the military to wage that campaign. 

Bush hasn't spelled out exactly what he seeks, but his administration has favored such new-generation military hardware as the Global Hawk, a long-range, high-altitude spy plane that has seen its first use in Afghanistan. 

The president was also pointing out that the transformation will cost money, aides said. 

His address comes as House-Senate bargainers begin writing a compromise $20 billion anti-terrorism bill to be attached to the $318 billion defense bill. 

The Senate bill contains an additional $2 billion for the Pentagon to use on construction and the war or terrorism. That's $5.3 billion less than Bush wanted and the GOP-controlled House approved. 

Defense Secretary Donald H. Rumsfeld argued that cutting the money Bush wanted for the Pentagon would "reduce our ability to sustain the operational intensity we will need in the effort to defeat terrorism" and would "send the wrong signal to our armed forces and our adversaries." 

The Senate approved its package by voice vote anyway. 

The Associated Press contributed to this report.