The White House is considering a ban on all prescriptions for barbiturates - the sleeping pills often known as "downers" - and restricting their use to hospitals, Dr. Peter Bourne, President Carter's special assistant on drug abuse, has disclosed.

He gave two reasons: the many overdose deaths these pills cause and the availability today of other, safer drugs to ease tension and promote relaxation.

Barbiturates are among the nation's most widely used drugs. More than 3 million prescriptions were written last year. Barbiturates are mainly used to induce sleep but are also used in treating epilepsy and some muscle problems.

Their use has dropped 38 per cent since 1974, however, because of growing awareness of their dangers and the existence of other drugs, a pharmaceutical source said.

"More persons die from barbiturates than all other drugs put together - suicides, accidental deaths of children who get them in medicine cabinets, inadvertent overdoses," Bourne said in a United Press International interview released yesterday.

"We've decided to look at whether we really need barbiturates now that there are many other drugs on the market that are much safer. We're going to be doing an extensive study to look at the possibility of taking barbiturates off the market on an out-patient basis."

But his office will also study whether there are conditions, such as epilepsy, for which barbiturate prescriptions may be "absolutely necessary," he added, and study the economic impact on pill-makers of such restrictions.

"We have no definitive position yet," explained Ellen Metsky, administrative assistant in the White House Office of Drug Abuse Policy.

"We'll actually be looking at three options - keeping barbiturates on the market and educating the public and physicians in their dangers, restricting them to hospital use, and taking them off the market entirely," she said.

Metsky was unable to estimate how long the studies could take.

Restrictions on barbiturates are "certainly worth considering," Dr. Paul Mazel, a pharmacology professor at George Washington University, commented yesterday.

"We do need them for certain things. Some epileptic children and adults must take them every day, and they're very effective," he said.

"Many physicians do believe they're also valuable for certain situations for short periods. But there has been increasing awareness of the problems.

"There's not only the overdose danger, but it also seems that barbiturates suppress 'REM' or 'rapid eye movement' sleep - the kind of sleep when you dream - and there is a rebound effect, that is, tension or agitation, when you stop taking these drugs."

The most widely used and probably safest drug to induce sleep without such severe problems is flurezepam or Dalmane, he said. Another commonly used "nonbarbituarate hypnotic" is glutethimide or Doriden, he said.

"Dalmane is the same class of compounds as the tranquilizers like Librium and Valium but a little more potent," Mazel said. "For a lot of people who can't sleep because of anxiety or tension they work pretty well. There are other drugs, too. But the only one that doesn't seem to be addictive is Dalmane."