WASHINGTON — House and Senate leaders have agreed to a new compromise surveillance bill that would effectively shield from potentially costly civil lawsuits telecommunications companies that helped the government wiretap citizens’ phone and computer lines after the September 11, 2001 terrorist attacks without court permission.

The House will debate the bill on Friday, potentially ending a months-long standoff about the rules for government wiretapping inside America.

The House Majority Leader, Steny Hoyer, a Democrat of Maryland, said the new bill “balances the needs of our intelligence community with Americans’ civil liberties, and provides critical new oversight and accountability requirements.”

The issue of legal protection for telecommunications companies that participated in “warrantless wiretapping” has been the single largest sticking point. The Senate passed a bill that immunized them from lawsuits. The House bill was silent on the matter. The White House threatened to veto any bill that did not shield the companies, which tapped lines at the behest of the president and attorney general — but without permission from a special court established for this very purpose — the Foreign Intelligence Surveillance Court.

“Warrantless wiretapping” went on for almost six years until it was revealed by the New York Times. Some 40 lawsuits have been filed against the companies by people and groups who think they were illegally eavesdropped on by the government.

The compromise bill would have a federal district court determine whether the telecommunications companies received signed orders authorized by the president asking them to place wiretaps to detect or prevent a terrorist attack. If so, the lawsuits would be dismissed.

But not all Democrats are falling in line.

The Senate Judiciary Committee Chairman, Senator Leahy, a Democrat of Vermont, said he does not support the immunity deal because it prevents a court from reviewing the legality of the warrantless wiretapping program.

A congressional official said he believes all the companies have such orders, and therefore all 40 cases would be dismissed. There was small chance of them progressing anyway; the Bush administration has stymied them by invoking its state’s secret privilege to bar evidence from being brought into court.

The compromise bill also requires several inspectors general to investigate the wiretapping program to determine its extent and legality. The report is due in a year.

The Foreign Intelligence Surveillance Amendment bill also would:

• Require FISA court permission to wiretap Americans who are overseas

• Allow the FISA court 30 days to review existing but expiring surveillance orders before renewing them

• Prohibit the government from invoking war powers or other authorities to supersede surveillance rules in the future.