Hatch was quoted in Tuesday's Tooele Transcript Bulletin as saying Middle East terrorists are "waiting for the Democrats here to take control, let things cool off and then strike again."
Democrats are criticizing Hatch for what they see as "ridiculous" partisan hyperbole.
"There they go again trying to use smear and fear to win in November," said Stacie Paxton, spokeswoman for the Democratic National Committee.
While Hatch now says he does not recall making the reported statement to the Tooele newspaper, it would not be the first time he tied terrorist action to Democrats seeking office.
During the 2004 presidential election, Hatch suggested al-Qaida members wanted Democratic challenger John Kerry to defeat President Bush.
Terrorists "are going to throw everything they can between now and the election to try and elect Kerry," Hatch said in a Washington Post story printed in September 2004.
Welcome to the politics of fear.
"Fear is a very powerful emotion," said Brigham Young University political scientist Kelly Patterson. "It is a powerful motivator. It is something that people understand and therefore politicians use it."
Earlier this week, Vice President Dick Cheney suggested that Connecticut Democrat Ned Lamont's primary victory over pro-Iraq War Sen. Joe Lieberman may encourage "the al-Qaida types."
Patterson said Republicans like Hatch and Cheney know they have an advantage when elections hinge on national security and defense issues. And despite polls showing a growing frustration with the Iraq war, Republicans appear to be sticking to the same methods that secured their power in the past election.
Patterson said Democrats would use similar tactics if the country were suffering from widespread disease or environmental disasters.
Hatch's challenger Democrat Pete Ashdown said the senator continuously goes too far.
The comment "is a further example of the demonization and the divisiveness Senator Hatch uses to win campaigns."
But Hatch said Wednesday he was only trying to reiterate a long-held position about Iraq. He clarified the statement through a spokesman, although he does not recall saying it.
"I don't believe terrorists favor Democrats or Republicans," Hatch said. "What they are waiting for is the United States to prematurely pull out of Iraq. There are appeasers in both parties but most are leading liberal Democrats."
While some Democrats, like Lamont, have called for a withdrawal, Ashdown said he wants the Iraqi people to decide if U.S. troops are still needed through a countrywide referendum.
Vermont Sen. Patrick Leahy regularly jousts with Hatch on the Senate Judiciary Committee.
Leahy's spokesman, David Carle, combated the perception that Republicans have kept America safe through their actions in Iraq.
"The gross mismanagement of the war in Iraq has handed the terrorists the biggest recruiting and training ground they have ever had, making us less secure than before," he said.