Alexandria Mayor Charles E. Beatley called yesterday for Charles T. Strobel, the city's director of public safety, to be placed on administrative leave after learning that federal authorities have begun a criminal investigation of the city's troubled police department.

No sooner had Beatley's request become public than a special grand jury that is inquiring into Strobel's handling of a 1984 drug investigation sent a letter to members of the City Council members urging them to delay any action against Strobel until their report is released.

"I think Charlie has some problems, whether they're criminal or managerial, I don't know," Beatley said in an interview. His comments came after he called on City Manager Douglas Harman to remove Strobel from day-to-day control over the city's police and fire departments.

Beatley also called an emergency meeting of the council at 7:30 a.m. today to get support for Strobel's suspension. The mayor said he decided to act early yesterday morning after reading in The Alexandria Journal that a federal grand jury was looking at other matters in the police department. The mayor and another source said yesterday that the federal grand jury is believed to be examining allegations that Alexandria police may have engaged in wiretapping in violation of federal laws.

Strobel, who joined the Alexandria force 26 years ago and rose to chief and then public safety director under Harman, declined through a spokesman to comment. David Fiske, Strobel's lawyer, said he did not know of any federal investigation of his client.

Harman, who has defended Strobel during two months of often-bitter controversy over the drug investigation, did not agree to the request. He said he did not think any action should be taken until the council had "explored issues like the legal liabilities of such an action." He said he asked City Attorney Cyril D. Calley to brief the council on that question today.

Calley said that the council does have to power under Alexandria's city manager form of government to seek Strobel's suspension, but cannot suspend him on its own directive. Harman, who has made no secret of his disgust at the current controversy, has resigned effective at midnight Tuesday to take a similar job in Fort Worth.

Beatley said that if Harman declines to put Strobel on leave he will ask the council to ask Vola Lawson, who becomes acting city manager Wednesday, to take the action.

Details of the scope of the federal investigation, which one source said began earlier this month, could not be learned yesterday. U.S. Attorney Elsie Munsell and an assistant, Justin Williams, who is said to be directing the inquiry, declined to comment.

Several people, some of whom have appeared as witnesses before the special Alexandria Circuit Court grand jury, are known to have talked with Williams about allegations concerning Strobel and past activities in the city police department. At least one of those who approached Williams testified before the federal grand jury the first week in February, a source said.

Harman said that after a meeting with Beatley yesterday morning he called Circuit Court Judge Donald H. Kent who impaneled the special grand jury Jan. 15 to ask him when the panel's report might be released. "What is the rationale for taking an action [against Strobel] just days before the grand jury makes its report?"

The grand jury's letter, which was delivered to city officials yesterday afternoon, said that "because of the imminent completion of this special grand jury's investigation, it is requested that you postpone taking any administrative action against Strobel . . . until a report is made . . . . We will recommend to Judge Kent that certain portions of our report be released to the public."

The letter said the request was "by unanimous consent" of the 11 members and was signed by the panel's foreman, Brett Chowning.

Beatley, who has long demanded that city officials conduct their own administrative inquiry into Strobel's agency, called the letter "improper and inappropriate." He said "I get the feeling that they're trying to say Charlie Strobel hasn't done anything wrong. His slate is clean."

Williams was asked to meet with the special grand jury this morning, according to a reliable source.

Meanwhile, the special grand jury, which is empowered under Virginia law to issue a report but not to indict, yesterday heard more witnesses. Arlington County Commonwealth's Attorney Henry Hudson and an Arlington detective, David G. Green, were among them, according to one source. Hudson's testimony concerned the status of a l971 murder of a Arlington man said to have been involved in prostitution.

Former Alexandria police detective Louis Pugh said he told the special grand jury laast week that in l974 Strobel had stopped him from following up reports that linked two policemen from another jurisdiction to the murder. Pugh has said Strobel, then head of inspectional services, did not give him a reason for ending the investigation.

Former Alexandria deputy police chief Clyde Scott Wednesday said that Pugh had complained to him in l981 about Strobel's actions.

Scott said in an interview he tried to discuss the matter in 1983 with Harman but was unable to get an interview with him. He said Strobel accused him of making an investigation of Pugh's allegations after Strobel had forced him out of his position as deputy chief. Scott denied making such an investigation.

Democratic councilman Donald C. Casey, who has pushed hard for an investigation of Strobel, said that the grand jury letter was an intrusion "on the political process that "is absolutely unprecedented . . . . I'm not inclined to back off."

Vice Mayor Patricia Ticer said, however, "I would certainly feel obliged to abide by the request of the special grand jury . . . there's no need for hurry.