Attorney General Dick Thornburgh, responding to new allegations of misconduct at the Department of Housing and Urban Development, has asked the independent counsel investigating former HUD secretary Samuel R. Pierce Jr. to significantly broaden the inquiry of Pierce's activities.

Thornburgh's request, made in a letter to independent counsel Arlin M. Adams released yesterday, would expand the scope of Adams's work to include administration of the Urban Development Action Grant program and of Pierce's discretionary fund.

Thornburgh had asked Adams to decide whether Pierce and other HUD officials may have engaged in a conspiracy to defraud the government through the moderate rehabilitation rent subsidy program between 1984 and 1988.

Thornburgh's actions were taken after investigators in the Justice Department's Criminal Division reviewed testimony former HUD official DuBois L. Gilliam gave a congressional subcommittee last month. In his letter to Adams, Thornburgh said Gilliam's statements are "related" to Adams's investigation.

"It would appear that in the light of the Gilliam testimony it may be appropriate to redefine the mandate of the independent counsel," Adams said. "I shall of course carefully consider this letter from the attorney general during the next few days and take action promptly."

Thornburgh's action followed three days of dramatic testimony by Gilliam in which the former HUD deputy assistant secretary described how Pierce routinely ordered his subordinates to fund grant applications for friends and associates without regard to the merits of the grants.

Gilliam also admitted receiving hundreds of thousands of dollars from developers while at HUD. He is completing an 18-month sentence at the Lompoc Prison Camp in California for accepting payments in exchange for the approval of a Biloxi, Miss., waterfront project. He is scheduled to be eligible for parole next month.

Gilliam testified that Pierce steered contracts to political allies who were down on their luck, to Hampton University while Pierce sat on the board of trustees, and to Gilliam himself as he prepared to leave the department in 1987.

Pierce's attorneys have questioned the credibility of Gilliam, who was granted limited immunity from further prosecution in exchange for testifying before a House Government Operations subcommittee.

"Mr. Pierce has done nothing wrong, period," said Pierce attorney Paul L. Perito. "We have nothing to fear by an impartial review of scurrilous allegations . . . as opposed to the hysteria and insatiable thirst for publicity of a congressional inquiry gone awry."

Members of the Government Operations subcommittee welcomed Thornburgh's action yesterday but said the investigation should be even broader.

Rep. Charles E. Schumer (D-N.Y.) said yesterday that Thornburgh should "issue a broad mandate and let the independent counsel's investigation go where the evidence warrants."

Schumer called on Adams to investigate whether Pierce had lied to the subcommittee in his testimony. But Rep. Christopher Shays (R-Conn.), who, along with other subcommittee members, had planned to ask Thornburgh to expand the investigation later this week, said a perjury probe would address only part of the problem.

"I have said from Day One, I don't want Pierce to get in trouble because he perjured himself," Shays said. "If he's done nothing wrong at HUD, then I think he shouldn't be in trouble."