The District government will perform what should be an ordinary municipal task Tuesday: It will hang a few street signs.

But that simple act will come amid an international minidebate starring an insistent U.S. senator, a reluctant State Department, city officials trying to obey the law, and Andrei Sakharov, the Soviet human rights activist who was released from internal exile in December.

Relatives of Sakharov said yesterday that the Soviet physicist told them this week "it would serve no useful purpose" to go ahead with a law sponsored by Sen. Charles E. Grassley (R-Iowa) to erect three signs on 16th Street NW -- including one in front of the Soviet Embassy -- to identify more clearly the one-block area as Andrei Sakharov Plaza.

Grassley is insisting that the District, whose budget is controlled by Congress, comply with the law, which was designed to create a symbol of resistance to Soviet repression of dissidents.

One small sign now exists, erected in 1985 about 100 feet from the embassy at 1125 16th St. NW. Grassley was responsible for the measure mandating that sign, too, but was dissatisfied when it was not placed in front of the embassy, city officials said. Under an amendment attached by Grassley to the District's current budget, the city must erect street signs at 16th and L streets and 16th and M streets, as well as directly in front of the embassy.

"I had a chance to discuss {this} with Andrei Sakharov and although he asked me to express his appreciation to Senator Grassley for his efforts . . . at the same time, he asked me to convey to the senator that he thinks at the moment, to move the sign closer to the embassy would serve no useful purpose," said Efrem Yankelovich, Sakharov's son-in-law who lives in a Boston suburb.

The State Department, which had objected to the single sign, has said the new signs would send the wrong signal to the Soviet Union just as it is displaying new openness, according to city officials. State Department officials yesterday declined to get involved in the public fray.

City officials said they believe naming streets should be a local function, not a congressional one. But they find themselves stuck in the middle.

"We don't want to get caught between a senator and the State Department," said Julius Hobson Jr., congressional liaison for Mayor Marion Barry. Hobson said the city has prepared the three new signs, but has not put them up in recent weeks because of the State Department objections. Finally, though, a law is a law.

"If we don't hang the signs, the city is subject to a civil suit," said Hobson.

Some city officials indicated privately that another reason for acting now to put up the signs is that Grassley was named in January to the Senate Appropriations subcommittee that passes on the city's $2.6 billion budget.

Aides to Grassley said yesterday that the senator wants to go ahead despite any new signs of openness from Soviet leader Mikhail Gorbachev, who has ordered the release of several Soviet dissidents.

"Given that the Sakharov sign was initially presented as a symbol, its significance today, in an era of glasnost {the Russian word for openness}, is probably more important now than ever before," Grassley said through a spokesman. Grassley contends that if the Soviets are serious about being a more open country, they might welcome the signs, aides said.

The aides also said that they had spoken recently with Sakharov's stepdaughter, Tatiana Yankelovich, and that she had conveyed a less hostile view than reported by Efrem Yankelovich. An aide said Tatiana confirmed that Sakharov thought the signs "would serve no useful purpose" but specifically answered "no" when Grassley aides asked her if the signs would hurt the Sakharov cause.