The White House conceded yesterday that there may have been the "appearance of impropriety" involved in the case of Bill Milliken, a close Carter family friend who interceded with the government for a developer who agreed to give $10,000 to a non-profit corporation Milliken runs.

But White House press secretary Jody Powell, reporting on the results of a White House inquiry into the matter, said the investigation turned up nothing to contradict Milliken's description of his intervention for the developer as "a mistake in judgment" that was "done innocently."

Powell indicated there will be no change in Milliken's relationship with the White House and, in response to questions, said no further action in the case is being considered.

Underscoring President Carter's strong support for Milliken, Powell said the president personally chose Milliken's Atlanta-based Institutional Development Corp. to participate in a federal pilot project that seeks improved coordination in the use of federal and private funds in community projects. Milliken, with Carter's approval, worked seven months last year as a consultant to the Office of Management and Budget in setting up the pilot project and was paid $13,000 by the federal government, he said.

The project is now run out of an office in the Old Executive Office Building next to the White House, Powell said. The use of that office by employes working on other of Milliken's nonprofit ventures has been "discontinued," he said.

The Washington Post reported last week that, earlier this year, Milliken interceded with federal housing officials on behalf of George Zamias, a wealthy Johnstown, Pa., developer seeking a $15.5 million federal grant for a shopping mall-apartment-hotel complex.

While discussing Zamias' efforts to obtain a federal grant, both men have acknowledged in interviews, Milliken solicited and later received a $10,000 contribution to the IDCI.

Milliken later called a friend in the administration, Richard Fleming, deputy assistant secretary of housing and urban development, who set up a meeting between Zamias and HUD officials, Zamias' grant application is still pending.

The IDC, part of the federal pilot project approved by Carter, contributes its own funds and obtains federal grants for a variety of urban educational programs. The project has received strong White House support.

Powell said Milliken's intervention on behalf of Zamias consisted of a single phone call to Fleming to ask Fleming to arrange a meeting with Zamias. He said other HUD officials, but not Fleming, attended the meeting with Zamias and public officials from Johnstown, including the city's mayor. Powell suggested that the meeting would have taken place without Milliken's intervention.

Asked if the White House had considered asking Milliken to return the $10,000, Powell said that "would strike me as a little harsh." He said nothing turned up in the investigation, conducted by White House counsel Robert Lipshutz, "indicated any violation of the law."

Milliken is widely known as a deeply religious man who heads several nonprofit corporations that provide assistance to inner-city children experiencing trouble in school and to street academies for dropouts and youths with personal problems.

His interest in these ventures attracted the attention of Rosalynn Carter, who is his strongest White House supporter and whose press secretary has described Milliken as an unpaid adviser to Mrs. Carter.