President Reagan, in what he acknowledged was an "extraordinary step," signed the independent counsel reauthorization into law yesterday despite what he said were his "very strong doubts about its constitutionality."

In a formal statement expressing his misgivings, Reagan said he decided to sign the bill "in order to ensure that public confidence in government not be eroded while the courts are in the process" of resolving the constitutional issues.

Backers of the measure had been expecting a veto and said they were surprised at the move. They said they were confident they could have mustered enough votes to override a veto and suggested that Reagan signed it to avoid such a defeat.

"I don't know how you sign a bill that you swear up and down is unconstitutional," said Rep. Barney Frank (D-Mass.), chairman of the House Judiciary subcommittee that handled the legislation. "It's very surprising."

The measure extends for five years the system of having court-appointed independent counsels investigate high-ranking government officials in order to avoid conflicts of interest that might result if the Justice Department conducted the inquiries.

Yesterday was the deadline for action by Reagan. The reauthorization bill was passed by overwhelming majorities in the House and the Senate and it had been sent to the White House 10 days earlier. Unless Reagan had chosen to veto it, it would have become law at midnight last night without his signature.

Attorney General Edwin Meese III has disqualified himself from the debate because his conduct is under investigation by two independent counsels, one in the Iran-contra affair and the other in the Wedtech scandal. But the Justice Department has assailed the special counsel system, publicly and in the courts, as an unconstitutional infringement on the prerogatives of the executive branch.

In his statement, Reagan voiced disappointment that "the Congress has not heeded these concerns, apparently convinced that it is empowered to divest the president of his fundamental authority to enforce our nation's laws."

"In fact," he continued, "H.R. 2939 {the reauthorization bill} contains a number of new provisions that aggravate the infirmities in existing law."

Reagan was apparently referring to new rules in the law that were designed to curb Meese's controversial administration of it. He has been accused of improperly sidestepping the preliminary FBI investigations that the law envisions, of using improper standards in deciding whether to seek court appointment of independent counsels, and of failing to disqualify himself in several cases where he had a personal involvement.

The president said that he fully endorsed "the goal manifested in the Independent Counsel Act of ensuring public confidence in the impartiality and integrity of criminal law investigations of high-level executive branch officials. Indeed, despite constitutional misgivings," Reagan asserted, "my administration has faithfully and consistently complied with all the requirements of the act."

But the law's goal, Reagan said, "may not justify disregard for the carefully crafted restraints spelled out in the Constitution." As officers exercising executive authority in the area of law enforcement, independent counsels, he maintained, "must be subject to executive branch appointment, review and removal. There is no other constitutionally permissible alternative."

Reagan said he was gratified that these issues are pending before the U.S. Circuit Court of Appeals here, in a case involving independent counsel Alexia Morrison's investigation of a former assistant attorney general. "We will continue to express our constitutional objections in that case as it moves through the courts," Reagan said.

Sen. Carl Levin (D-Mich.), chairman of the Senate subcommittee that worked on the legislation, said that in signing the bill, "the president has avoided another confrontation with the Congress -- one I am confident he would have lost. . . . It was the wise course to follow."