The Justice Department, facing a budget shortfall, has ordered its 93 U.S. attorneys to begin no new investigations that involve travel or legal expenses for the next two months.

In an internal memo, the department also told its chief prosecutors to stop using computer research services, limit travel for ongoing investigations, seek to delay court cases, buy no new equipment and reduce orders for court and grand jury transcripts until the 1986 fiscal year ends Sept. 30.

Department spokesman Terry H. Eastland said the limit on new investigations would apply mainly to routine cases. "Obviously, if there's a major case or a dramatic terrorist explosion, you would investigate and prosecute," he said.

Although the cost-cutting measures are intended to be temporary, Eastland said, they could grow worse if a fiscal 1987 budget freeze approved by the House last week takes effect in October. He accused House leaders of "cutting into essential law-enforcement areas" while calling for an escalation in the war on drugs.

Attorney General Edwin Meese III had previously maintained that the first round of Gramm-Rudman-Hollings cutbacks this year had little impact on law enforcement. But the U.S. attorneys' offices lost $13 million in the process and still face a $1.3 million deficit.

The July 25 memo from William P. Tyson, head of the Executive Office for U.S. Attorneys, said that "all possible measures" must be taken to cut costs. "No new investigative or prosecutorial activities should be undertaken which necessitate expenditure of travel or litigation expenses this fiscal year," the memo said.

Such expenses, Tyson said, "shall be strictly limited to that amount essential for the conduct of imminent litigation. Travel for investigative and other purposes shall be deferred until October. Continuances should be sought when possible." He also ordered that air-conditioning and heating be turned off during overtime hours.

Joseph E. diGenova, the U.S. attorney here, said he would seek clarification of the new restrictions on investigations. "If these kinds of cuts continue for a long period of time, there would certainly be an effect on law enforcement ," he said. "Right now people are treading water effectively, but I don't know how long they can continue to do that."

Breckenridge L. Wilcox, U.S. attorney in Maryland, said he has been unable to replace experienced prosecutors because of a 2-month-old hiring freeze on U.S. attorneys' offices. "It's hurt me a lot . . . . I will likely be deferring some long-term investigations," he said.

But Wilcox said he would try to "do business as usual. People get arrested all the time. We have busts of dope deals all the time, and those can't be put in the deep freeze."

The U.S. Marshals Service has been forced to limit overtime pay for transporting prisoners and guarding witnesses, leading to trial delays, spokesman Stephen Boyle said. He said the department is tracking down fewer fugitives and that under the House budget for next year, "There will be at least 3,000 more fugitive felons on the streets than there would have been. These are bad guys, people who have been convicted of serious crimes from murder on down."

The House amendment, sponsored by Rep. Bill Frenzel (R-Minn.), essentially froze the Justice Department's $4.1 billion budget for fiscal 1987 by slicing 5 percent from most accounts. The House voted to exempt the FBI and Drug Enforcement Administration.

While most divisions received level funding or slight increases, the House bill cut President Reagan's request for U.S. attorneys from $353 million to $322 million, and contained similar reductions for the Immigration and Naturalization Service, Marshals Service and Bureau of Prisons.

Frenzel is trying to freeze each appropriations bill because "we think most of these accounts can stand a marginal cut," an aide said. "We don't think you make reductions painlessly."

But Rep. Neal Smith (D-Iowa), chairman of the subcommittee that controls the Justice budget, said: "What good does it do to catch a drug pusher if you don't have a U.S. attorney to prosecute him, and there aren't enough jail cells to put him in jail?" And Eastland complained that the House bill includes $125 million more than Reagan requested for grants to researchers and local governments.