The House overwhelmingly passed a new independent-counsel bill yesterday and sent it to the White House, where officials said that President Reagan will be urged to veto it.

The Senate had approved the measure before Thanksgiving, and the House vote on final passage was 322 to 90.

Republican opponents of the measure echoed Justice Department contentions that the measure is unconstitutional because it provides for court appointment of special prosecutors in cases involving high-ranking administration officials.

Backers of the bill, which would renew and strengthen current law for the next five years, pointed out that Reagan signed it without any reservations when it was last reenacted in 1982.

Rep. Barney Frank (D-Mass.) charged that the only thing that has happened since then to make it unconstitutional was that "a lot of appointees of President Reagan" have come under investigation.

Put into final form last month by House-Senate conferees, the measure includes a number of new rules designed to counteract Attorney General Edwin Meese III's controversial administration of the statute.

Under the law, the attorney general is supposed to set the independent counsel process in motion by ordering a preliminary FBI investigation whenever he receives "specific" information from a "credible" source alleging criminal conduct on the part of a high-ranking government official.

If this limited, 90-day inquiry shows "reasonable grounds" for further investigation, the attorney general must apply to a special three-judge federal court for appointment of an independent counsel.

The congressional committees in charge of reauthorizing the law said Meese had gutted the 90-day deadline, used improper standards in squelching some cases and shown an "extremely troubling" tendency not to disqualify himself from several cases where he had a personal involvement.

Rep. Patrick L. Swindall (R-Ga.) argued that the system not only intrudes on the separation of powers doctrine but amounts to a virtual "bill of attainder" in singling out a certain class of individuals to be treated differently.

Rep. George W. Gekas (R-Pa.) said he, too, regarded the bill as unconstitutional but wanted it amended to cover members of Congress automatically, drawing gibes from Frank, who asked Gekas why he wanted to extend the mandatory coverage if it was in danger of being nullifed by the courts.

"I want it to be unconstitutional as to everybody," Gekas replied. "It is the only fair way to do it."

Frank and other Democrats pointed out that under the law, the attorney general has the option of seeking independent counsels to investigate members of Congress if there is any conflict of interest posed by having the Justice Department conduct the probe.

The Justice Department and the Office of Management and Budget are expected to recommend a veto, but White House spokesmen say Reagan has yet to make a decision.