Al Qaeda's network has weakened, but the U.S. must continue to step up efforts to thwart its outreach and prevent possible attacks perpetrated by its followers, three terrorism investigators told the House Select Intelligence Committee on Wednesday.

However, pulling troops out of Iraq to target the terror group in Afghanistan and Pakistan, where Al Qaeda's stronghold remains, may not be the best solution, the witnesses testified.

This is "a very difficult problem" to resolve, said Peter Bergen, a senior fellow at the New America Foundation. Bergen advised that the U.S. must target Al Qaeda's "safe havens," where the training of militants occurs. He added that the network's main fronts continue to reside in both Pakistan and Afghanistan.

But if the United States withdraws its troops, he said, it would enable Al Qaeda to establish safe havens in the country where it could more effectively strategize and carry out operations. On the other hand, if the U.S. maintains a military presence, he cautioned, it will continue to radicalize Al Qaeda's followers in Iraq and elsewhere.

The witnesses appearing at the hearing denied Al Qaeda's existence in Iraq prior to the U.S.-led invasion.

“Al Qaeda in Iraq is an Iraqi phenomenon,” said Robert Grenier, director of Kroll, Inc.

The experts also agreed that while Al Qaeda continues to pose a serious threat, it cannot be effectively defeated unless it is viewed within a broader context.

"It’s my basic contention that we cannot decouple Al Qaeda from the larger battle of Islamic terrorism. We cannot afford to isolate the problem to only that of Al Qaeda. It’s imperative that we look at the larger problem of radical Islamic ideology," said Steve Emerson, Director of the Investigative Project on Terrorism, a terror watchdog group.

The non-governmental officials were appearing before the panel just hours after a top Al Qaeda leader linked to the July 2005 London bombings was reported dead.

Abu Ubaida al-Masri, an Egyption national and senior operative within the terrorist organization, is believed to have died several months ago in Pakistan, perhaps from hepatitis, U.S. counterterrorism officials told FOX News.

Al-Masri is credited with recruiting, training and directing the suicide bombers involved in the July 2005 London bombers, and officials also believe he played a role in the liquid explosives bomb plot to blow up transatlantic flights bound for the U.S. and Canada in the summer of 2006. He is not a household name, but considered one of the terror groups top 10 leaders and very senior within the organization.

As the seeming good news reached American shores, the House panel's chairman said he does not believe the Bush administration has a winning plan to defeat Al Qaeda.

"Al Qaeda has the freedom to recruit, the freedom to train, and the freedom to plot new attacks against the United States," said Rep. Silvestre Reyes, D-Texas. "Clearly, the threat from Al Qaeda in the Afghanistan-Pakistan border region is real, and frankly, I’m not confident that the administration has a winning plan to defeat the Al Qaeda threat, despite the efforts of our men and women in the intelligence community, as well as those in our military and diplomatic corps."

Among the most difficult challenges posed by Al Qaeda's leadership is its hydra-like nature —- as top Al Qaeda operatives are knocked off, new militants continually emerge. The probability of "Al Qaeda central" extending its reach and influence is also a difficulty. Emerson said radicalism is "pervasive" and must be continuously and aggressively monitored, even in the U.S. and Western Europe.

“We have a serious radical Islamic danger in the United States,” he said.