The House of Representatives has launched a review of its security procedures in the wake of the arrest of a District man who allegedly tried to pass copies of secret House documents to the Soviet Union, House General Counsel Steven Ross said yesterday.

Ross said House officials were considering having all closed hearings transcribed by stenographers on the House staff, rather than turning to outside reporting firms, or, if outside firms are used, making checks of security procedures in use at the firms.

"The House is conducting a review of security procedures and whether or not we can continue to rely on the security clearances that are done by the Department of Defense," Ross said. "From the facts that have been reported on this incident . . . I think we will certainly institute some procedures to provide a little bit of a double check."

Acme Reporting Co., the firm where the arrested man, Randy Miles Jeffries, worked as a messenger, said in a statement yesterday that it had undergone a routine Defense Department check of its security procedures less than three weeks ago "and no problems or deficiencies were found involving document safekeeping."

At a hearing yesterday, U.S. Magistrate Jean F. Dwyer warned prosecutors that they needed "more meat" to buttress the government's "bare bones" allegations against Jeffries.

According to an FBI affidavit filed in federal court here yesterday, Jeffries took a stack of classified documents from the company earlier this month and told a coworker he "needed to find a Russian to sell the documents to."

In the affidavit, the FBI said agents searching Acme on Saturday, the day after Jeffries' arrest, discovered numerous classified documents, marked "secret" and "top secret," ripped in four pieces and placed in a plastic trash can.

The affidavit stated that an unnamed Acme official "advised that the company maintains copies of top secret and secret documents in its safe. These documents are disposed of by ripping them by hand and placing them in the trash."

According to Defense Department regulations, classified material is supposed to be destroyed by shredding or burning. Two employes are supposed to witness the destruction of top secret material, and "the destruction process must be sufficient to preclude recognition or reconstruction of the classified information."

L. Britt Snider, the Defense Department's director of counterintelligence and security policy, said that the statements in the FBI affidavit about security procedures at Acme, if true, "raise some questions about the security practices" of Acme. He said the company would be reinvestigated shortly.

The Defense Investigative Service reviews clearances for individuals who handle classified information at the reporting companies and inspects the facilities themselves to make certain there are adequate security precautions in place.

A Pentagon commission studying security practices concluded in a report released last month that the service was "seriously understaffed," with 225 inspectors to review 13,000 companies cleared to handle classified information.

Acme Board Chairman Charles L. Richer said in an interview that "what has been published is nowhere near the truth. We don't rip them classified documents up and dispose of them in public."

A source familiar with the Jeffries case said the documents he tried to sell to the Soviets were transcripts of closed hearings of the House Armed Services Committee. Acme has a contract with the committee under which Acme personnel who hold security clearances transcribe the hearings if none of the reporters on the House staff are available to cover it.

Ross said there are 12 in-house reporters, but only half hold security clearances. Clearances for the rest are pending, he said, but some have been waiting for as long as a year to get approval to hear classified information.

He said 85 to 90 percent of the closed hearings are handled by the in-house staff.

In addition to its work for the Armed Services Committee, Acme transcribes hearings for the House Foreign Affairs Committee, the Veterans Affairs Committee and several other committees, Ross said.

The arrest of Jeffries highlighted a concern about security procedures on Capitol Hill that has been building in recent months and that is part of an increased attention to security throughout the government and among private contractors in the wake of the recent wave of espionage arrests.

Senate Intelligence Committee Vice Chairman Patrick J. Leahy (D-Vt.) said yesterday he believes that all classified hearings in the Senate should be transcribed in-house. Except for the Intelligence Committee, Senate committees have all their transcription work done by outside firms.

"I think in the Senate we would be well-advised to have three or four people who would be given the most rigorous of security clearances by the FBI and who would do all their work on the Hill in a secure area," Leahy said. "No method is foolproof, but that at least eliminates some of the obvious dangers."

While the reporters for outside firms may hold security clearances, Leahy said, "it's the handling of the material, and the security of the material is not as good as it would be if we did it here."

Senate Governmental Affairs Committee Chairman William V. Roth Jr. (R-Del.) said, "I think it can be fairly said that committee and personal offices vary very widely in their handling of classified material . . . . To me what the immediate case shows is how pervasive the problem is. Congress loves to criticize everybody else, but we ought to take a look at our practices as well."

In June, Roth and Sen. Sam Nunn (D-Ga.), ranking minority member of the Governmental Affairs investigations subcommittee, released a set of security recommendations including instituting a set of general standards and practices for handling classified information on Capitol Hill.

A report issued last month by a Pentagon commission studying security problems found that "little attention is given the handling and storage of such information by congressional staff." The commission, headed by retired Army Gen. Richard G. Stilwell, also recommended the adoption of "rules to provide uniform minimum control over classified information" provided to Congress.

House Intelligence Committee Chairman Lee Hamilton (D-Ind.) said he urged both houses to review security precautions. "So far as I know we now operate with the Armed Services Committee handling it their way, the Foreign Affairs Committee handling it in their manner -- they operate on security questions independent of one another. In light of what has occurred . . . I think that the security procedures on the Hill probably need extensive review."