The Obama administration on Wednesday toned down harsh criticism of Pakistan leveled by the outgoing chairman of the Joint Chiefs of Staff but made clear that it expects more counterterrorism cooperation from Islamabad if tenuous ties are to improve.

The softening in rhetoric came as some in Pakistan reacted angrily to Adm. Mike Mullen's remarks claiming formal concrete links between the Haqqani insurgent network and Pakistan's main intelligence service, which have triggered a nationalist backlash, whipped up media fears of an American invasion and threatened to further complicate already tense relations.

The White House, Pentagon and State Department carefully refused to endorse comments from Adm. Mike Mullen that the Haqqani network "acts as a veritable arm" of Pakistan's Inter-Services Intelligence agency, or ISI. But officials at all three buildings allowed that the U.S.-Pakistan relationship is fraught with frustrating complications and said counterterrorism cooperation must improve.

"I have no argument with anyone who says this is a very difficult and complex relationship because it is," Secretary of State Hillary Rodham Clinton told reporters at the State Department. "But I also believe strongly that we have to work together despite the difficulties."

At the White House, press secretary Jay Carney said Mullen's statement was "not language I would use." But he said the comment is "consistent with our position" and tried to dismiss questions about it as a "matter of semantics." He reiterated that the Haqqani network has safe havens in Pakistan and Pakistan needs to take action to address that.

Pentagon press secretary George Little said Defense Secretary Leon Panetta agreed that elements of the Pakistani government, including the Inter-Services Intelligence agency, "appear to provide support and facilitation to the Haqqanis." Little would not comment more specifically; he referred reporters to Panetta's testimony at the Senate hearing where Mullen made his comments.

Mullen himself, in remarks to The Wall Street Journal published Wednesday, said that while the ISI has supported the Haqqani network, it does not necessarily control details of the group's operations.

"It is very clear they have supported them," Mullen told the Journal. "I don't think the Haqqanis can be turned on and off like a light switch. But there are steps that could be taken to impact the Haqqanis over time."

Clinton said the urgency of improving cooperation was underscored by the recent attack on the U.S. Embassy in Kabul by the Pakistan-based Haqqani network, which has also carried out numerous attacks Pakistani soil. Pakistan, she said, faces an even greater threat from the Haqqanis and al-Qaida than does the United States.

"It is important to realize that while it is not always easy, the United States and Pakistan have vital strategic interests that converge in the fight against terrorism," Clinton said.

She added that the State Department was in the final review process of designating the entire Haqqani network a "foreign terrorist organization," which would hit all members of the group with U.S. financial and travel sanctions. At the moment, only the group's top leaders have been designated as terrorists and slapped with sanctions.

There have been numerous calls from Congress for those individual designations to be boosted with a group designation.

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AP Military Writer Robert Burns contributed to this report.