The terrorists who beheaded Berg wanted to "shake" America's resolve in bringing democracy to Iraq, Mr. Bush said.
"The actions of the terrorists who executed this man remind us the nature of a few people who want to stop the advance of democracy," Mr. Bush told reporters on the South Lawn of the White House as he left for an education speech.
"Their intention is to shake our will," Mr. Bush said. "Yet by their actions they remind us of how desperately parts of the world need free societies ... We will complete our mission, we will complete our mission."
Berg's body was found near a highway overpass in Baghdad on Saturday, the same day he was beheaded, a U.S. official said. A Web site on Tuesday posted video in which he identified himself and was beheaded by masked men who claimed the killing was revenge for the.
According to his family, Berg, a small telecommunications business owner, spoke to his parents on March 24 and told them he would return home on March 30. But he was detained by Iraqi police at a checkpoint in Mosul on March 24.
The family says Berg was turned over to U.S. officials and detained for 13 days.
On April 5, the Bergs filed suit in federal court in Philadelphia, contending that their son was being held illegally by the U.S. military.
The next day Berg was released, the family said. He told his parents he hadn't been mistreated. His family last heard from him April 9 but it was unclear when and where he was abducted.
His father, Michael Berg, told the British Daily Telegraph newspaper that his son's detention might have made it harder for his son to escape Iraq before he was swept up in escalating violence.
But coalition spokesman Dan Senor said Wednesday that Berg was never under U.S. custody despite claims from his family.
Senor told reporters that Berg, 26, from West Chester, Pennsylvania, was detained by Iraqi police in Mosul. The Iraqis informed the Americans and the FBI met with Berg three times to determine what he was doing in Iraq.
Senor said that to his knowledge, "he (Berg) was at no time under the jurisdiction or detention of coalition forces."
An FBI statement states, on March 25, "the U.S. military notified FBI Agents in Iraq that the Iraqi Police had detained a U.S. person in Mosul, Iraq. The U.S. person was identified as Nicholas Evan Berg. Mr. Berg had been detained by Iraqi Police who then notified the U.S. military."
However, calls by The Associated Press to police in Mosul failed to find anyone who could confirm Berg was held there or why.
The FBI release further states, "During interviews with Mr. Berg, FBI agents and CPA officials emphasized to him the dangerous environment that exists in Iraq, and encouraged him to accept Coalition Provisional Authority's (CPA) offer to facilitate his safe passage out of Iraq. Mr. Berg refused these offers. The CPA coordinated with the Iraqi police for Mr. Berg's release on April 4. He also refused government offers to advise his family and friends of his status."
Senor said "multiple" U.S. agencies would be involved in the Berg case and that the FBI would probably have overall direction.
Senor said that in Iraq, Berg had no affiliation with the United States government, the coalition or "to my knowledge" any coalition-affiliated contractor.
Earlier, a U.S. official, speaking on condition of anonymity, said Berg was in Iraq "of his own accord" and had been advised to leave Iraq but refused.
Berg's family said they were informed by the State Department on Monday that he was found dead.
When told by a reporter about the Web site, Berg's father, brother and sister grasped one another and slowly dropped to the ground in their front yard, where they wept quietly while holding each other.
"I knew he was decapitated before," Michael Berg said. "That manner is preferable to a long and torturous death. But I didn't want it to become public."
Berg's body arrived back in the United States today.
An official at a funeral home says Berg's family members are welcoming the news that his body arrived back home today.
Authorities had said earlier that Berg's remains were being flown to the military mortuary at Dover Air Force Base in Delaware. It's not far from Berg's home in West Chester, Pennsylvania.
A memorial for Berg is planned on Friday.
The video in which Berg was killed bore the title "Abu Musab al-Zarqawi shown slaughtering an American," referring to an associate of Osama bin Laden believed behind a wave of suicide bombings in Iraq.
It was unclear whether al-Zarqawi was shown in the video or simply ordered the execution. Al-Zarqawi also is sought in the assassination of a U.S. diplomat in Jordan in 2002. The United States has offered a $10 million reward for information leading to his capture or killing.
The decapitation recalled the kidnapping and videotaped beheading of Wall Street Journal reporter Daniel Pearl in 2002 in Pakistan.
Last month, Iraqi militants videotaped the killing of Italian hostage Fabrizio Quattrocchi, but the Arab TV network Al-Jazeera refused to air it because it was too graphic.
Friends and family of Berg said he— working in Ghana, in one example — and that his going to Iraq fit with that ideology. They said he supported the Iraqi war and the Bush administration.
"He was so upbeat about the things he was witnessing in Iraq. And he wanted to be part of that rebuilding process using his skills," David Skalish, a longtime friend of the victim, told CBS News' Early Show.