House-Senate conferees agreed yesterday to renew the independent counsel law for five years and to adopt rules designed to curb Attorney General Edwin Meese III's controversial administration of the statute.

The Senate immediately passed the bill, 85 to 7. The House is expected to approve it after returning from Thanksgiving recess.

Rep. Barney Frank (D-Mass.), the manager of the House conferees, said he expects President Reagan to veto the measure but predicted that there would be enough votes to override such action.

"If they're at all consistent, they'll veto it," Frank said yesterday. The Justice Department has denounced the system of providing for court-appointed prosecutors to investigate high-ranking officials as unconstitutional. None of the changes made by the conferees would cure that basic complaint. As Frank put it, "It's still unconstitutional according to the Justice Department."

A White House spokesman said no final decision has been made, but he confirmed that both Justice and the president's Office of Management and Budget are expected to recommend a veto. Aides to Sen. Carl M. Levin (D-Mich.), the Senate manager of the bill, said they hope White House chief of staff Howard H. Baker Jr. will argue against such advice.

"He was here {in the Senate} during Watergate," one Levin aide said. "He knows how important it is."

The law will expire Jan. 2 unless it is reauthorized. But even expiration will not affect the criminal investigations and prosecutions of past and present Reagan administration officials under way. A special provision in the statute protects "pending matters" such as the Iran-contra investigation, the inquiry into Meese's conduct in the Wedtech scandal, the trial of former White House deputy chief of staff Michael K. Deaver, and the forthcoming prosecution of former White House aide Lyn Nofziger.

Meese testified yesterday for the third time before the federal grand jury investigating the Iran-contra affair under the direction of independent counsel Lawrence E. Walsh. The attorney general was harshly criticized earlier this week in the final report of the congressional Iran-contra committees for his handling of the initial, pre-Walsh inquiry into the scandal last year.

Meese has been the target of repeated complaints by the subcommittees, headed by Levin and Frank, that reviewed his and the Justice Department's administration of the independent counsel law.

Under the law, the attorney general is supposed to launch a 90-day preliminary inquiry upon receipt of "specific" information from a "credible" source alleging criminal conduct on the part of a high-ranking government official. If this limited inquiry shows "reasonable grounds" for further investigation, the attorney general is required to apply to a special three-judge federal court for appointment of an independent counsel.

The congressional subcommittees said Meese had "essentially eviscerate{d}" the 90-day deadline with a device that the Justice Department calls a "threshold inquiry" and which it says it uses to determine if the information is "specific" and "credible" enough.

In one case, the Justice Department took seven months before determining, secretly, that no further investigation was needed. In another case, involving former deputy attorney general Edward Schmults, Meese said the "principal basis" for not seeking an independent counsel was "lack of evidence of criminal intent on the part of Mr. Schmults," a conclusion that lawmakers said Meese had no business making.

Levin's subcommittee also found Meese's failure to disqualify himself from the intial Iran-contra inquiry and other cases, such as that of Schmults, a man Meese had known for 20 years, "extremely troubling."

The conferees agreed on new rules that would limit threshold inquiries to 90 days, prohibit "state of mind" findings except in the rarest of cases, and require the attorney general to disqualify himself in any case involving someone with whom he has "a current or recent personal or financial relationship."

At the same time, the conferees abandoned a House provision that would have allowed an independent counsel to go directly to the special court for broader jurisdiction and agreed on a Levin proposal to give the attorney general exclusive authority in such instances.

Frank said he acceded on that issue reluctantly and plans to return to it next year if it becomes a problem.