Citing "scraps of intelligence," Rumsfeld also renewed his accusation that Syria provided Iraq with night-vision goggles and other military technology.
Meanwhile, fighters from Syria and other Arab countries moved into Iraq to join the resistance against the U.S.-led coalition.
State Department spokesman Richard Boucher said the United States has made it "quite clear in a number of statements that we don't think anybody should be aiding a dying regime."
On Capitol Hill, Reps. Eliot Engel, D-N.Y., and Ileana Ros-Lehtinen, R-Fla., said they would seek action on legislation authorizing President Bush to punish Syria through curbs on exports and the sale of equipment with military use, and restrictions on Syrian diplomats' travel in the United States.
"Now that Saddam Hussein's regime is on the precipice of defeat, it is time for America to get serious about Syria," Engel said.
Rumsfeld, at a Pentagon news conference, said that according to intelligence, "Syria has been cooperative in facilitating the movement of people out of Iraq into Syria, and then in some cases, they stayed there and found safekeeping there."
In other cases, he said, "they are moving from Syria to still other places."
Rumsfeld provided no details.
Later, he told reporters on Capitol Hill that he was not referring to highest level Iraqi officials.
"These are regime-type people" about whom U.S. officials have "intelligence scraps" suggesting they are heading toward Syria, he said.
"I didn't want anyone to get excited and think that we're talking about very senior, senior people," he said after a closed-door briefing with House members.
Sen. Saxby Chambliss, R-Ga., said, however, "there is a cause for concern about what may be going on within Syria so far as official support for Saddam's regime."
But "there's nothing definitive there," said Chambliss, a member of the Senate Intelligence and Armed Services committees. "You're talking about tens of people, not thousands of people."
At the State Department, a senior official said Rumsfeld may have referred, in part, to reports that some Iraqi scientists had been given refuge in Syria and that Iraqi military in western Iraq had slipped back and forth across the border.
The State Department has urged Syria to stop any movement of people or technology across the border to Iraq. Syria has responded with assurances the border is closed to everything but humanitarian goods, the official said on condition of anonymity.
Last week, Secretary of State Colin Powell demanded that Syria stop supporting terrorism.