The attorney for one of the two segregated private schools that the Reagan administration promised to grant tax-exempt status to last month said yesterday he will ask the Supreme Court not to dismiss the case because the government hasn't fulfilled its pledge.

Administration sources acknowledged that the Internal Revenue Service is dragging its feet in granting the exemptions to Goldsboro Christian Schools Inc. in Goldsboro, N.C., and Bob Jones University in Greenville, S.C. Neither is likely to be granted an exemption soon, the sources said, because of concerns about additional bad publicity and the precedent that would be established if the government gave up a victory won in the lower court.

The 4th U.S. Circuit Court of Appeals ruled last year that the IRS had properly denied exemptions to the two schools and that they were liable for hundreds of thousands of dollars in back taxes.

William G. McNairy, who represents Goldsboro, said in a telephone interview from North Carolina that his client is concerned that the government has not granted it a tax exemption, as it told the Supreme Court on Jan. 8 it would.

"We don't want the cases dismissed until we get the relief we asked for," McNairy said. "We plan to ask the Supreme Court not to vacate the cases until the government does what it promised."

Late yesterday afternoon McNairy said he received a call from Joel Gerber, deputy chief counsel at IRS, saying he'd be receiving a letter and "implying we'd have to fill out an application for an exemption." McNairy said that wouldn't satisfy his client's fears because the application "could be buried in bureaucratic red tape for months."

Goldsboro and Bob Jones University were challenging the IRS' denial of their exemptions when the administration unexpectedly reversed a 12-year-old IRS policy on Jan. 8, saying the law didn't specifically exclude exemptions for segregated private schools. The government told the Supreme Court that the exemptions would be granted to the two schools so the cases should be dismissed as moot.

"The Department of Treasury has initiated the necessary steps to grant petitioner Goldsboro Christian Schools tax-exempt status," the government said in its papers asking the Supreme Court to vacate its victory in the appeals court. The filing added that Treasury "has commenced the process necessary to revoke forthwith" the revenue rulings used to deny the two schools exemptions.

The high court has been in recess and hasn't decided yet whether to dismiss the cases as moot.

After a storm of protest from civil rights groups, the president backtracked and proposed legislation for a retroactive ban on the exemptions to Goldsboro, Bob Jones and other segregated private schools. In the meantime, the IRS said it would process only the exemptions for the two schools, leaving 300 pending applications in limbo.

Congress, however, has made no move to enact the legislation. And now Goldsboro is worried about the government's inaction.

Philip Murren, an attorney for Bob Jones, said his client hasn't received any word from the IRS about its promised exemption either.

An IRS spokesman said he didn't think there was any great delay in processing. "We're doing what we need to do," he said. But sources said the IRS is stalling, despite the administration's position at the Supreme Court.