WASHINGTON (CNN) -- Republicans have seized on a liberal advocacy group's print ad attacking Gen. David Petraeus and have called on Senate Majority Leader Harry Reid to denounce it.

Gen. David Petraeus listens to opening statements Monday before testifying at a congressional hearing.

In the ad, running in Monday's edition of The New York Times, bold letters under a picture of Petraeus spell out "General Petraeus or General Betray us?"

MoveOn.org Political Action, which paid for the ad, accuses Petraeus of "cooking the books for the White House" on progress being made in Iraq and calls him "a military man constantly at war with the facts."

Petraeus on Monday began giving an assessment to Congress about the progress of the war in Iraq.

A letter addressed to Reid circulated Monday among senators asking that Reid make it clear he does not share MoveOn.org's views.

The letter reads: "The ad is distasteful and frankly, below the level of respect that America's commanding general in Iraq has earned. No matter whether any senator supports or opposes the war in Iraq, we should all voice recognition and appreciation of Gen. Petraeus' long and distinguished record of service to our country."

A senior Democratic leadership aide called the ad an "unnecessary distraction" and said Democrats are prepared to focus on "Petraeus executing a mismanaged mission."

House Minority Leader John Boehner, R-Ohio, said, "Democratic leaders must make a choice today: Either embrace the character assassination tactics Moveon.org has leveled against the four-star general leading our troops in the fight against al Qaeda, or denounce it as disgraceful."

"Gen. Petraeus and the other commanders in the U.S. Armed Services have dedicated their lives to defending the very freedom that enables MoveOn.org the right to free speech. I support that right, but I find the way they have chosen to exercise it today to be disrespectful and downright reprehensible," Boehner said in a statement.

Sen. Joe Lieberman, I-Connecticut, also called on the Democratic leadership to "denounce MoveOn.org's attack on Gen. Petraeus." Lieberman has been supportive of President Bush's efforts in Iraq.

Congressional Democrats showed an eagerness to distance themselves from the ad.

Asked early Monday if this was the right message for his party to send, a member of the Democratic leadership, speaking on background, curtly answered, "No."

Sen. John Kerry, D-Massachusetts, called the ad "over the top."

"I don't like any kind of characterizations in our politics that call into question any active duty, distinguished general who I think under any circumstances serves with the best interests of our country," said Kerry, the 2004 Democratic presidential candidate and a decorated veteran.

"I think there are a lot of legitimate questions that need to be asked, a lot of probing that ought to take place; there's a lot of legitimate accountability that needs to be achieved. It ought to be done without casting any aspersions on anyone's character or motives," he added.

White House spokesman Tony Snow called the ad, running the same day the general testified before Congress about Iraq, a "boorish, childish, unworthy attack."

MoveOn.org said Monday it stood by the ad completely.

"Every major independent study and many major news organizations cast serious doubt on Petraeus' claims," said Eli Pariser, executive director of MoveOn.org Political Action Committee.

"It should come as no surprise that Gen. Petraeus' claims have come under critical scrutiny: The facts all point in one direction -- the surge isn't working -- and Gen. Petraeus and the White House are pointing in another," the statement said.

"No wonder recent polls show that the American people agree with the ad also: A majority expect that the general will deliver 'a biased report that reflects what the Bush administration wants the public to believe,' " the statement said, quoting from a USA Today/Gallup poll reported in Monday's USA Today. E-mail to a friend

CNN's Dana Bash, Mark Preston and Alexander Mooney contributed to this report.

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