The Alexandria City Council rejected yesterday Mayor Charles E. Beatley's call for the immediate suspension of Public Safety Director Charles T. Strobel, whose police department is being investigated by both city and federal grand juries.

The mayor got the support of only one of his six fellow council members at a special early-morning meeting he had called, and some criticized him for calling the session on short notice when a regular meeting is scheduled for today.

With Strobel and his wife Paula sitting in the audience, the council was asked to delay action by Robert F. Horan Jr., chief Fairfax County prosecutor, who is special counsel to the special city Circuit Court grand jury probing police department practices. "Suffice it to say," he said, "that some of what you have read in the newspapers is just not supported" by testimony and documents placed before the jury. He said the jury probably will make its report within a week.

Horan's remarks to the council yesterday and a letter the grand jury sent to council members late Thursday, also urging them to delay action, fueled speculation that the jurors have not found evidence of wrongdoing by Strobel.

On Thursday, Beatley called for City Manager Douglas Harman to place Strobel on administrative leave after a local newspaper, the Alexandria Journal, reported that a federal grand jury also is probing matters in the police department. The mayor scheduled yesterday's meeting to solicit the council's support for the move, since Harman did not agree to the request.

The city grand jury has heard testimony from about 30 witnesses over four weeks in a probe apparently centering on allegations, widely reported in the media, that Strobel mishandled a drug investigation.

Horan said the 11 members of the panel asked him to appear before the council, and he called the jurors "a credit to the city," praising them for diligence and having "a sense of fairness."

Under the city's charter, the council can advise and discuss personnel actions with the city manager, but cannot carry them out. Harman, who has been Strobel's mentor during his nine years as city manager, has stoutly defended him.

Harman will leave Alexandria to take up the post of city manger in Fort Worth next week. Vola Lawson, who will become acting city manager of Alexandria, has declined to say whether she would suspend Strobel.

Beatley, a Democrat, saw two of his Democratic supporters, Lionel Hope and Vice Mayor Patricia Ticer, agree with the council's three Republicans that any recommendations from the council about Strobel's future should wait until they receive the special grand jury's report.

Hope said that the letter from the special grand jury and Horan's appearance "are saying that if we had done what we started to do, we would have made a mistake."

Beatley's only supporter was Democratic Councilman Donald C. Casey, who has pushed for a council investigation of the police department. A formal vote was not taken.

Even Beatley's Democratic allies were perplexed by his action in calling the special meeting. "I don't know why we could not have discussed it" at the regular Saturday meeting, said Ticer. The mayor, she said, is "supersensitive to this issue."

Afterwards Beatley would not admit defeat, saying his goal had not been a vote all along, but an opportunity to "get internal discussion of the council . . . on the table. I wanted people to know how we feel. We're in an election year. This is important." Beatley, who is seeking reelection, has no announced opposition in the May election.

He said he still feels strongly that "the issue is whether the police department, from a management standpoint, should be put on hold while we go about some research and evaluation" into its practices.