Ten members of the D.C. Council announced support last night for a bill limiting the District's mayor to two consecutive terms in office, a measure that its sponsor said was needed to deal with "the loss of public confidence in our government."

The bill, introduced by council member Frank Smith Jr. (D-Ward 1), would create a special category for Mayor Marion Barry, now in his third term, allowing him to run for one more term if he chooses in 1990. But the measure was seen by some council members and their staffs as a move to distance the council from the mayor, whose administration has been the subject of wide-ranging investigations by the U.S. attorney's office and the FBI.

Despite Smith's contention that the move was not directed at Barry, knowledgeable Barry administration officials said the bill will be seen by some people as criticism of the mayor. "If you're going to limit the mayor, why not limit the chairman {of the council} or limit the council members?" said one administration official.

A council member, who asked not to be identified, said, "It seems to be a repudiation of the mayor. The timing is such that it could cause political damage . . . . It would be seen as adversarial and would inflame the entire executive branch."

In a statement, Smith declared that "a perpetual term in office can compel the executive to willingly exchange endless favors in order to ensure reelection." He added: "Public perception shifts, no longer viewing the populist hero as a shining example of the American success story; years of cronyism create cynicism."

Council member Charlene Drew Jarvis (D-Ward 4), one of the three members who did not cosponsor the bill, said she opposed it on policy grounds and because its timing could be widely seen as political.

Dwight Cropp, director of intergovernmental relations for the mayor, said Smith discussed the proposal with Barry two weeks ago. Cropp said the mayor did not endorse the measure or oppose it but "had no problem" with Smith introducing the bill. Smith strongly endorsed the mayor in his successful race for a third term in 1986.

But Barry's aides privately questioned why Smith, a longtime Barry associate, would bring up the sensitive succession issue at a time when the administration is facing serious questions, involving not only federal investigations of the city but also key changes in the makeup of Barry's staff. It was reported this week that longtime City Administrator Thomas M. Downs is a finalist for a major transit post in Philadelphia.

Council Chairman David A. Clarke, who also refused to cosponsor the bill, said the issue should be put before D.C. voters in a referendum. "Legislation of this sort could be viewed as self-serving if undertaken by the council alone," said Clarke, who strongly considered mounting a challenge to Barry in last year's Democratic primary.

But Smith, who has been friend of Barry for 25 years, said a referendum on the proposal "would wind up as a referendum on Marion, and that would be unfair to him and unfair to the public." Smith added that a referendum "would give a skewed result. I think he would win. He's still popular."

In recent months, Barry's administration has not only been the subject of grand jury probes but also has been criticized by members of Congress, which has final authority over the District's budget and laws despite the 13-year-old home rule charter.Staff writer Tom Sherwood contributed to this report.