Mayor Marion Barry yesterday ordered a freeze on hiring and promotions in the District government and prohibited most overtime pay and out-of-town trips for city employes at the first phase of his plan to close a city budget gap of at least $84 million.

The order, which will take effect tomorrow, was designed to help cut city spending by reducing the District payroll. Budget director Gladys W. Mack said some layoffs also may be necessary to carry out the desired number of reductions, which are expected to be detailed early next week.

According to one source, Barry met with a group of city officials for severals hours yesterday and discussed a group of proposals that could account for about $84 million of the deficit, including $11 million saved in personnel reductions and other spending cutbacks.

A larger part of the package, however, would require tax increases, which are almost certain to provoke controversy. The mayor refused to say yesterday which taxes might be raised.

As much as $25 million in new or increased city taxes and higher fees for city services was under discussion at one point, according to the source. Higher property taxes (now among the lowest in the area) and sales taxes (now among the highest in the area) and a possible new tax on the services of professionals and persons in trade such as barbers and beauticians were discussed.

A key Barry aid said that increasing the city's income tax is most undesirable because it would take money out of everyone's pocket during a time of inflation and would probably create the greatest political problem for the mayor, who won office by a narrow plurality.

Barry said yesterday that he is considering deferring a decision on how to fill the largest single item in the budget deficit -- $48.5 million in potential refunds and lost revenues from a professionals tax ruled illegal earlier this year.

The D.C. Court of Appeals ordered the city to pay back $41 million already collected and forbade the collection of another $7.5 million it had expected to collect this year.

On Wednesday, however, the city asked the U.S. Supreme Court to review the lower court's decision. That action could suspend for several months any requirement that the city comply with the appeals court order.

Even after the matter is decided, Barry said yesterday, the city would not know definitely how much money it would need since many persons who paid the professionals tax are expected to find the potential refunds too bothersome to request.

Therefore, several aides said, a proposal that the city wait until the litigation is completed and then borrow the funds necessary to make the refunds was under consideration yesterday.

Budget director Mack refused to say yesterday how much the city hopes to save from the job freeze or how many jobs are to be eliminated from the work force. Earlier she had estimated that about 1,000 positions would have to be vacated, either through attrition or layoffs.

The city's troubled public school system would not be covered by the freeze, nor would the court system. Both operate somewhat independently of the mayor's office.

Yesterday's order also exempts an estimated 13,000 city jobs financed through federal grants, such as the Comprehensive Employment and Training Act (CETA) program.

In addition to new hiring, the order also prohibits transfers and details from one agency to another, but it allows exemptions to be made in order to avoid "serious disruption of program operations."

Acting personnel director Jose Gutierrez said that in the police, fire and corrections departments, as well as in some parts of the Department of Human Services, more exemptions are likely to be granted, and hiring would be considered on "a case-by-case basis."

The general ban on overtime also makes exceptions for the police, fire and corrections departments, which are politically sensitive because of concern about public safety. The order also permits overtime pay for employes of DHS, many of whom work longer hours in order to keep city institutions staffed around the clock.

Police investigators are the only city employes exempted from the ban on out-of-town travel, which is designed to pare expenditures estimated to be more than $1 million a year.

Barry also imposed a limited freeze on supply and equipment purchases, rental of new space, employe training expenditures and outside consultant services.

Essential items such as food, fuel, drugs and medical supplies are exempted from this ban, even though cost increases for some of them have been key contributors to the city's overextended financial situation.

The official unveiling of Barry's plan is to come next week, after he returns from a weekend trip to Richmond and Knoxville, Tenn. Aides said the mayor is making both trips at his own expense.