WASHINGTON—The White House’s decision to distance itself from Adm. Mike Mullen’s criticism of Pakistan for harboring terrorists could seriously hurt the U.S.-Pakistan relationship without improving counterterrorism efforts, according to experts at the Council on Foreign Relations.

At last week’s Senate Armed Forces Committee hearing, Mullen, chairman of the Joint Chiefs of Staff, called the Haqqani network, a subgroup of the Afghanistan insurgency based in Pakistan, a “veritable arm” of the Pakistani military, and blamed it as well as Pakistan’s Inter-Services Intelligence Agency for the Sept. 14 attacks on the U.S. embassy in Kabul.

Daniel Markey, a senior fellow for India, Pakistan and South Asia at the Council on Foreign Relations, said Wednesday that Mullen’s statement’s implied an ultimatum: If Pakistan doesn’t take significant steps to counter the threat posed by the Haqqani network and sever its ties with the network, the U.S. would be prepared to escalate its actions to combat the group.

Markey said he was surprised that the White House didn’t back Mullen’s comments.

“Unfortunately … I’ve been hearing sounds within the administration suggesting that not everybody was on board with that tougher tone,” Markey said.

White House Press Secretary Jay Carney said at a press briefing that Mullen’s comments were not “language I would use,” but that it is clear that Pakistan has not tried to eliminate safe havens for the network in the country.

Markey said taking a tougher stance on Pakistan is only worth it if the U.S. government is unified behind the idea.

“If it’s not, then really what you have is a poisonous statement with nothing to back it up,” Markey said. “We’ll end up with a worse relationship and no positive benefits on the counterterrorism and counterinsurgency side.”

But Ed Husain, a counterterrorism expert at the Council on Foreign Relations, said the publicity about Mullen’s comment on Pakistan’s support for the Haqqani network undermined the point of his overall statement. What Mullen was really trying to do was advocate a strong relationship with Pakistan, Husain said.

Markey said he expects Congress will pass legislation to set conditions on further U.S. military aid to Pakistan.

“It is difficult on Capitol Hill to argue against the observation that Pakistan is in any way helping terrorists or killing Americans and that we shouldn’t be in the business of providing them money,’’ he said.  “At some level, Mullen has changed history by taking the steps that he did.”

But cutting aid would just make it harder for to the White House to get Pakistan to sever its ties with the Haqqani, Markey said.

“My sense is that the (Pakistani) public would respond very poorly and it would accelerate a broader rupture between our two countries,” he said.

Husain said decreasing or halting military aid to the area could result in a perception among Pakistanis that the U.S. is abandoning their country at a critical junction.

“Yes [Pakistan] has made mistakes and yes they’ve haven’t been the most loyal and staunch allies,” he said. “But in their eyes, it will seem as though the U.S. … was not able to complete its mission.”

He said the military aid is the only leverage the U.S. has with Pakistan so “the U.S. should not be backing away but should actually be getting close to Pakistan.”