House Majority Leader Jim Wright (D-Tex.), responding to allegations of illegal drug use and sexual favors among congressional pages, said yesterday that the present unsupervised living conditions of the pages is intolerable and asked for immediate construction of "an official page dormitory."

Wright said in a statement issued by his office that he knew of the problem because "on one occasion" he was told that a page he had sponsored "had been experimenting with drugs" and that Wright made sure "he was off the page rolls" and on his way home that evening.

"It is absolutely impossible under the present circumstances to guarantee wholesome supervision or even personal safety" to pages, Wright said.

On Thursday, the House Committee on Standards of Official Conduct, informally known as the ethics committee, announced that it was investigating allegations of drug trafficking among pages.

The committee also is probing what Wright termed "even more shocking allegations that some members of Congress have abused their positions to demand sexual favors from these young people."

The Justice Department has been investigating allegations of drug use and illegal sexual activities involving pages and members of Congress stemming from reports provided the FBI by two former pages, according to sources on Capitol Hill.

The focus of the investigation, sources have said, is not sexual preference, but whether members of Congress and congressional staffers had sexual relations with minors or promised pages advancement in return for sexual favors.

In addition, a federal grand jury here in Washington is looking into allegations that a cocaine ring operated on Capitol Hill, using pages, elevator operators and other congressional staffers.

The roughly 70 House and 30 Senate pages are appointed by members of Congress and a few top Capitol Hill officials. Some House members said yesterday they have not sought to name pages because unsupervised life in Washington is too difficult for many of the teen-agers.

An aide to Rep. Pat Schroeder (D-Colo.) said yesterday that the congresswoman has decided to stop naming pages. It was a Schroeder page who first told the FBI of alleged drug use and sexual activities.

At present, there is only one building available for housing male pages, the U.S. Capitol Page Alumni Association building at 625 East Capitol St. It has room for up to 15 pages. The 40 other male pages must find their own living quarters.

Almost all female pages are housed in a Capitol Hill building that is also occupied by other women, but an aide in the office of the House doorkeeper would not provide the address.

Wright said it was "gross negligence" that Congress has delayed authorizing long-standing plans for "an official John W. McCormack Page Dormitory," with the proposed facility named for the former House speaker.

There is an "appropriate site" for the building near to the Capitol and owned by the government, Wright said. It could be built "within months" and financed by rents equivalent to those now being paid to private landlords.