Mr. Bush said he might contact Syrian leaders on Sunday to make clear his warning. His comments followed Defense Secretary Donald H. Rumsfeld's assertion that "there's no question" that some senior Iraqi leaders have fled to Syria.
The president did not say he was threatening military action against Iraq's western neighbor, but said of the Syrians: "They just need to cooperate."
Secretary of State Colin Powell also warned Syria not to harbored members of Saddam Hussein's regime.
In a broadcast interview, Powell said, "We have designated Syria for years as a state that sponsors terrorism." He warned that it would be unwise if Syria "suddenly becomes a haven for all these people who should be brought to justice."
Rumsfeld said some Iraqi leaders remained in Syria, while others have moved on to different countries. He declined to identify the Iraqis or the other countries, or if the United States was prepared to take any punitive action against Syria.
"We certainly are hopeful Syria will not become a haven for war criminals or terrorists," Rumsfeld said.
Saddam's half brother, Watban Ibrahim Hasan, an adviser to the Iraqi president, has been captured by U.S.-led forces, a U.S. official said Sunday. He was planning to cross the border to Syria, said the official, speaking on condition of anonymity.
Busloads of Syrians have entered Iraq to fight against the U.S.-led coalition, Rumsfeld said. Some of them have been turned back to Syria, others have been captured and still others have been killed in firefights, he said.
Syrians accounted for the largest share of foreign fighters that U.S. troops have faced in Baghdad over the past 24 hours, he said.
U.S. troops captured one bus filled with Syrians as well as several hundred thousand dollars in cash and "leaflets suggesting that people would be rewarded for killing Americans," Rumsfeld said on CBS' "Face the Nation."
Syria's deputy ambassador to the United States, Imad Moustapha, denied that his country was harboring escaped Iraqis. In a broadcast interview he said it was the responsibility of U.S. troops to monitor Iraq's western border with Syria.
Powell said Iraq's progress toward democracy could be an example to countries like North Korea and Iran, which "have systems which are certainly not friendly to democratic principles, who have supported terrorist activities over the years, and who have been developing and even possess weapons of mass destruction."
On Saturday, a top Pentagon adviser who is considered an architect of the policy that led to the war with Iraq issued a stark warning to Syria on Saturday.
Richard Perle, a member of the influential Defense Policy Board, told the International Herald Tribune that if Syria were found to be hiding Iraqi weapons, "I'm quite sure that we would have to respond to that."
"But I suppose our first approach would be to demand that the Syrians terminate that threat by turning over anything they have come to possess, and failing that I don't think anyone would rule out the use of any of our full range of capabilities," Perle said.
The remark is one of several by top U.S. officials and advisers in recent weeks that suggest the U.S. might turn the heat up on Damascus now that Baghdad has fallen.