A briefcase full of documents that may have been crucial evidence in the espionage case against a District man charged with passing secret House documents to the Soviet Union has been destroyed, the accused man's lawyer told a federal magistrate yesterday.

U.S. Magistrate Jean F. Dwyer ordered Randy Miles Jeffries, a messenger for a stenographic company that transcribes secret proceedings of the House Armed Services Committee, to be held without bond pending federal grand jury deliberations on charges that he delivered and attempted to deliver national defense secrets to the Soviets.

Shortly before his arrest Friday night, Jeffries, 26, told an FBI undercover agent posing as a Soviet operative that he had left with a "trusted friend" a locked briefcase containing three classified documents, an FBI agent testified in federal court here yesterday.

Defense lawyer G. Allen Dale told the magistrate that he had met Monday night with an unnamed individual who said he had received the briefcase in question, did not know what it contained, and destroyed it "at the suggestion of someone on the phone." Dale said outside the court that the destruction took place before Jeffries' arrest.

In ordering Jeffries held without bond, Dwyer said she could not be sure the documents had been destroyed and that "leaves us with an unanswered question, and one that I dare not answer incorrectly," in case the papers still exist and Jeffries tries to pass them to the Soviets.

One of the documents Jeffries allegedly offered to sell the undercover agent was a top secret transcript of a hearing before a House Armed Services subcommittee about command, control, communications and intelligence programs, C3I.

According to papers filed in court yesterday, the transcript of that hearing was prepared by the Acme Reporting Co., where Jeffries worked, and "contains testimony of high-level Defense Department officials."

Command, control, communications and intelligence -- pronounced "Cee-Cubed-Eye" in the Pentagon -- is one of the military's most secret program areas and, in the nuclear field, one of the Reagan administration's top priorities. The administration named an assistant secretary of defense for C3I, Donald C. Latham, and the Pentagon has spent billions of dollars modernizing the systems.

In layman's terms, strategic C3I means "the button" and all the systems needed to make the button work in a crisis. Embraced by the term are the radars, satellites and other systems that would detect an enemy missile attack; the command centers from which a U.S. nuclear strike would be controlled, including the NORAD mountain fortress in Colorado and the flying command plane kept on constant alert; and redundant communications systems to pass orders from the president through his military commanders to the missile silos, bombers and submarines that would launch an attack.

Some material relating to C3I is mundane and well known, and even matters discussed in closed committee hearings often contain few secrets. But much about the strategic C3I system is considered extremely sensitive, because it involves U.S. nuclear war plans, intelligence capabilities and the vulnerabilities of communication systems.

At the hearing, Dale contended that the government lacked proof that Jeffries either delivered classified documents or tried to deliver them, other than Jeffries' own uncorroborated statements, which alone would be insufficient to convict him.

Dwyer, who at a hearing Monday described the government's evidence as "about as thin" a case as she had seen in recent years, said yesterday, "Frankly, I don't see that the case has gained very much weight overnight."

But she cited the statement of a co-worker of Jeffries' at the Acme Reporting Co. that he had seen Jeffries leave the firm with a stack of classified documents under his coat a few hours before a man matching Jeffries' description was seen entering the Soviet Military Office at 2552 Belmont St. NW. "That in itself gets us past the probable cause, but just barely," Dwyer said.

U.S. District Judge Joyce Hens Green last night denied Jeffries' appeal of the decision to hold him without bond. She said in a five-page order that government testimony "provided substantial probable cause to believe" that Jeffries had committed espionage and that the "weight of evidence against the defendant is persuasive."

Assistant U.S. Attorney Rhonda Fields argued that the case was "very strong," including videotapes of Jeffries at a meeting with an FBI undercover agent posing as a Soviet in which Jeffries allegedly offered to sell the agent classified documents and admitted giving the Soviets samples of the documents on two other occasions.

At the hearing, FBI agent Michael Giglia testified that Kevin Collins, a co-worker of Jeffries at Acme, told agents he had seen Jeffries leaving the company at 1220 L St. NW, with classified documents on Dec. 14. He said Jeffries told him he wanted to contact the Soviets to sell the documents, Giglia said.

Later that day, at 4:11 p.m., a "sensitive source" overheard a telephone call from a person identifying himself as "Dano" to the Soviet Military Office, offering to sell documents to the Soviets. Dwyer refused to let Giglia answer a defense question about the nature of the source, but Dale said later he could not think of any way the FBI would have known about both sides of the telephone conversation other than by intercepting the call.

At 4:45 p.m., a man fitting Jeffries' description was seen entering the office, and stayed there for about 30 minutes, Giglia testified. He said the cab driver who brought the man to the office later told the FBI he had picked up the passenger in the 200 block of Rhode Island Ave. NW, a block away from Jeffries' home at 143 Rhode Island Ave. NW.

Three days later, Giglia testified, the "sensitive source" reported that Dano had called the military office to inquire "if a decision had been made yet."

On Dec. 20, Giglia said, an FBI agent posing as a Soviet official telephoned Jeffries' home. He said the agent, who identified himself as "Vladimir" and who spoke with a Russian accent, asked Jeffries if he was Dano and if he remembered visiting the military office.

Jeffries answered "uh huh" to both questions, Giglia testified. He said, however, that Jeffries was suspicious of the call because he had been given a "contact plan" for a meeting in April and a "code word" to be used for identification. Jeffries nevertheless agreed to meet the agent at 9 p.m. at the Holiday Inn.

He said Jeffries told the agent that he had met with the Soviets twice, the first time giving them 13 pages each of three documents, and the second time another 15 pages. At the second meeting, he said, the Soviets said the documents "were good material and they were interested in them."

Jeffries was arrested at 9:11 p.m. as he was leaving the room, allegedly to pick up the classified documents to sell to the purported Soviet agent, Giglia said. He said no classified documents were found in a search of Jeffries' home, although about 20 books and brochures about the Soviet Union were found there.