WASHINGTON, Sept. 13— Hoping to prevent future terrorist attacks, House and Senate lawmakers expressed broad support today for funneling more money to intelligence operations, beefing up spy networks and creating one agency to handle terrorism.

The nation spends an estimated $10 billion a year to fight terrorism, a sum that many lawmakers from both parties called inadequate and that is likely to be increased this session. But instead of using the money to upgrade traditional satellite capabilities and telephone surveillance, many urged that the money be spent on old-fashioned human spying and more advanced computer tracking, the kind of intelligence that may have been able to prevent Tuesday's attacks.

''We need to re-emphasize the importance of getting a human being who can get inside those cells and learn what their intentions and capabilities are,'' said Senator Bob Graham, Democrat of Florida, the chairman of the Senate Intelligence Committee. ''We have also seen a reduction in the ability to eavesdrop on terrorists and others who might threaten the United States as the technology has changed. It was easier when they were communicating by telephone. It is more difficult when they are using computer communication.''

Mr. Graham and other lawmakers, speaking at news conferences and in interviews, said that just as important was the need to consolidate power to combat terrorism in one central agency or individual, a step that could alleviate dozens of existing jurisdictional battles.

''We need to have within our intelligence agency somebody specifically in charge of our counterterrorism efforts,'' Mr. Graham added. ''Today that responsibility is spread among a number of agencies and we spend too much time trying to decide just who is in charge.''

Representative Porter J. Goss, Republican of Florida, chairman of the House Permanent Select Committee on Intelligence, said Tuesday's terrorist attacks required a long-term commitment. ''The world is different,'' he said. ''Technology is different. The nature of the threat is different. The response must be different.''

The lawmakers' statements followed an acknowledgment by officials at the government's intelligence agencies -- the C.I.A., the F.B.I. and the National Security Agency -- that they were surprised by Tuesday's attacks. While the agencies have been criticized for what some have called an egregious lapse, many lawmakers believe that the agencies have been hamstrung by increasing restraints.

The issue over how to beef up intelligence is likely to begin in earnest over the next few weeks, when Congress votes on a bill to finance the Justice Department and grapples with military spending.

The ideas for revamping the intelligence agencies are wide-ranging. Some lawmakers, like Senator Evan Bayh, an Indiana Democrat who is on the intelligence panel, suggested that the C.I.A. should be given freer rein to stop terrorism, including reinstating its power to assassinate.

''It's not possible to seize him and bring him to trial,'' Mr. Bayh said, referring to Osama bin Laden if he turns out to be culpable. ''You can argue that a more targeted approach may be in order.''

Others talked of expanding domestic eavesdropping, an idea that makes those concerned about civil liberties uncomfortable.

Late tonight, the Senate approved an amendment as part of a spending bill to finance the Justice Department that would make it easier for law enforcement to wiretap computers and combat cyberterrorism. Supporters of the bipartisan amendment said law enforcement officials must go from jurisdiction to jurisdiction to obtain a court order since computer communication crosses state boundaries. The amendment would streamline the process by allowing a federal judge to issue an order.

After the vote, the Senate passed the larger bill to finance the departments of Commerce, State, Justice and the judiciary.

''You cannot tap the lines of a terrorist,'' said Senator Orrin G. Hatch of Utah, the senior Republican on the Judiciary Committee. ''This corrects that.''

The amendment caused concern among some senators who felt it was being rushed to the floor with little concern about giving the government new power to pry into someone's computer.

Congress is also expected to act to enhance airport security. For years, the House and the Senate have been reluctant to increase spending on better baggage inspections and X-ray machines, among other things, despite the advice of the General Accounting Office, the investigative arm of Congress. Now some lawmakers are urging the government to handle some portions of airport security, rather than permitting airports to hire private contractors.

Senator Ernest F. Hollings, Democrat of South Carolina, the chairman of the Commerce Committee, said the federal government should operate airport security scanners.

Unless that is federalized, he said, the government cannot expect to improve its current results.

One intelligence analyst who works for the government but asked to remain anonymous said none of these suggestions were new. The government has been aware of its intelligence gaps, he said; many became obvious during the bombing of two United States embassies in Africa and of the U.S.S. Cole in Yemen.

''People know what the solution is,'' the expert said. ''We haven't had leadership from either inside or outside to do it. It's a bureaucracy that won't get out of its own way.''