The nation’s top intelligence officials said Tuesday that al-Qaeda’s affiliates have eclipsed the terrorist network’s core as national security threats and that, within two years, continued pressure could render al-Qaeda remnants in Pakistan incapable of carrying out attacks.

Michael G. Vickers, the undersecretary of defense for intelligence, said at a defense conference that if the current pace of U.S. operations continues, “within 18 to 24 months, core al-Qaeda’s cohesion and operational capabilities could be degraded to the point that the group could fragment.”

Vickers’s remark represents the first time that a senior U.S. official has offered a time frame for achieving the collapse of the organization responsible for the Sept. 11, 2001, attacks. His comments were consistent with assessments delivered to Congress on Tuesday by the nation’s top two intelligence officials.

In his first public testimony as CIA director, David H. Petraeus said that the killing of Osama bin Laden and subsequent operations have opened “an important window of vulnerability for the core al-Qaeda organization in Pakistan and Afghanistan.”

Petraeus and Director of National Intelligence James R. Clapper Jr. stressed that al-Qaeda continues to plot attacks, and that its regional affiliates in Yemen and elsewhere have emerged as a lethal new threat to the United States.

Petraeus described al-Qaeda in the Arabian Peninsula, one of the affiliates, as “the most dangerous regional node in the global jihad” and said that the CIA has seen new signs of “al-Qaeda’s efforts to carry out relatively small attacks that would . . . generate fear and create the need for costly security improvements.”

Their testimony came during a rare joint hearing by the House and Senate intelligence committees that was meant to serve as a status report on al-Qaeda and U.S. counterterrorism efforts on the 10th anniversary of the Sept. 11 attacks. The last time the two committees held a joint session was in 2002, when they collaborated on the first major investigation of the intelligence failures related to the attacks.

Vickers, a former CIA officer who rarely speaks publicly, appeared separately at a conference at the National Defense University at Fort McNair.

Overall, officials said, the United States is better protected from terrorist strikes by strengthened security measures and a sweeping overhaul of the intelligence community, including the creation of the Office of the Director of National Intelligence, during the past decade.

“Are we safer today? The answer, I believe, is an unqualified yes,” said Sen. Dianne Feinstein (D-Calif.), chairman of the Senate Select Committee on Intelligence. Feinstein said that counterterrorism efforts appear to be gaining momentum and that U.S. operations against al-Qaeda in recent months have meant “more killed in rapid succession than at any time since Sept. 11.”

Clapper said U.S. spy agencies have dramatically improved their ability to share information and coordinate operations against terrorist groups. But he stressed the need for further changes at a time when the agencies are facing budget cuts after years of massive spending increases.

“I view this as a litmus test for this office — to preside over the difficult cuts we’re going to have to make,” Clapper said.

His testimony came as insurgents mounted an assault on the U.S. Embassy in Kabul on Tuesday and as al-Qaeda leader Ayman al-Zawahiri issued an audio message asserting that the Sept. 11 attacks helped set the stage for the toppling of autocrats in the Middle East this year.

Petraeus said that pressure on al-Qaeda and Taliban elements in Pakistan — driven mainly by the CIA drone campaign — may lead some mid-level al-Qaeda members to “seek safe haven across the border in Afghanistan or decide to leave South Asia.”

Critics have questioned whether Petraeus, who recently retired from the U.S. military after leading the war effort in Afghanistan, could offer impartial analysis of that conflict. His remark raised the possibility that al-Qaeda may seek to return to the country it fled when the war began.

Separately, Petraeus also disclosed that the CIA’s inspector general has opened an investigation into the agency’s relationship with the New York Police Department. The agency’s work with the department was the subject of a recent investigative report by the Associated Press.