WASHINGTON — The nation’s top military official said Thursday that Pakistan’s spy agency played a direct role in supporting the insurgents who carried out the deadly attack on the U.S. Embassy in Kabul last week. It was the most serious charge that the United States has leveled against Pakistan in the decade that the U.S. has been at war in Afghanistan.

In comments that were the first to directly link the spy agency, the Directorate for Inter-Services Intelligence, with an assault on the United States, Adm. Mike Mullen, the chairman of the Joint Chiefs of Staff, went further than any other U.S. official in blaming the ISI for undermining the U.S. effort in Afghanistan. His remarks were certain to further fray America’s shaky relationship with Pakistan, a nominal ally.

The United States has long said that Pakistan’s intelligence agency supports the Haqqani network, based in Pakistan’s tribal areas, as a way to extend Pakistan’s influence in Afghanistan. But Mullen made clear that he believed that the support extended to increasingly high-profile attacks in Afghanistan aimed directly at the United States.

These included a truck bombing at a NATO outpost south of Kabul on Sept. 10, which killed at least five people and wounded 77 coalition soldiers — one of the worst toll for foreign troops in a single attack in the war — as well as the embassy assault that killed 16 Afghan police officers and civilians.

“With ISI support, Haqqani operatives planned and conducted that truck bomb attack, as well as the assault on our embassy,” Mullen said in a hearing of the Senate Armed Services Committee. “We also have credible evidence that they were behind the June 28th attack against the Intercontinental Hotel in Kabul and a host of other smaller but effective operations.”

In short, he said, “the Haqqani network acts as a veritable arm of Pakistan’s Inter-Services Intelligence agency.”

His remarks were part of a deliberate effort by U.S. officials to ratchet up pressure on Pakistan and perhaps pave the way for more U.S. drone strikes or even cross-border raids into Pakistan to root out insurgents from their havens. Military officials in the U.S. refused to discuss what steps they were prepared to take, although Mullen’s statement made clear that taking on the Haqqanis had become an urgent priority.

On Thursday, Rehman Malik, Pakistan’s interior minister, rejected accusations by the United States of ISI involvement in the attacks in Afghanistan. “If you say that it is ISI involved in that attack, I categorically deny it,” he said in an interview with Reuters. “We have no such policy to attack or aid attack through Pakistani forces or through any Pakistani assistance.”

He also said his government would “not allow” a U.S. operation aimed at the Haqqani network in North Waziristan, a remote part of Pakistan’s lawless tribal region.

Malik seemed to indicate that U.S. officials had threatened on Tuesday in meetings in Washington with the head of the ISI, Maj. Gen. Ahmed Shuja Pasha, that U.S. troops were prepared to cross the border from Afghanistan to attack Haqqani militants. A U.S. official would say only that David H. Petraeus, the new director of the Central Intelligence Agency, told Pasha that the CIA would continue its campaign of drone strikes against the Haqqanis in Pakistan and pursue them in Afghanistan.

“The Pakistan nation will not allow the boots on our ground, never,” Malik said in an interview with Reuters. “Our government is already cooperating with the U.S. — but they also must respect our sovereignty.”

A senior U.S. official said Thursday that no decisions had been made on actions that the Obama administration might take against the Haqqanis.

Covert raids by the U.S. into Pakistan are rare — only two, including the raid that killed Osama bin Laden in May, have become public — but some U.S. intelligence officials argue that more aggressive ground raids in Pakistan are necessary. The United States gives Pakistan more than $2 billion in security assistance annually, although this summer the Obama administration decided to suspend or in some cases cancel about a third of that aid this year. Altogether, about $800 million in military aid and equipment could be affected.

The suspension was intended to chasten Pakistan for expelling U.S. military trainers this year and to press its army to fight militants more effectively. It was also decided after the bin Laden raid in Pakistan, where the leader of al-Qaida had been living comfortably near a top military academy.

Mullen is to retire at the end of this month, and coming from him the statements carried exceptional weight. For years he has been the U.S. military official leading the effort to improve cooperation with the Pakistanis. But relations have reached a nadir since the bin Laden raid. Officials in Pakistan were angered that they had not been told of the raid in advance, and questions remain about whether Pakistan’s intelligence was sheltering bin Laden.

Although U.S. military officials believe that the ISI is in many cases directing the Haqqani network to attack United States forces in Afghanistan, they did not go so far as to say on Thursday that the ISI specifically directed the assault on the U.S. Embassy. U.S. military officials did not describe the kind of support they believe the ISI gave the Haqqani network for the embassy attack, and also offered no evidence for their claim. In July 2008, the United States was able to determine that the ISI was behind the bombing of the Indian Embassy in Kabul based on intercepted communications of ISI officers.

Mullen testified alongside Defense Secretary Leon Panetta, who told the committee that the attack on the embassy and the assassination this week of Burhanuddin Rabbani, the leader of Afghanistan’s High Peace Council and a former president of Afghanistan, were “a sign of weakness in the insurgency.” He cast the attacks as signs that the Taliban had shifted to high-profile targets in an effort to disrupt the progress that the U.S. military had made.