The House and Senate enacted the District of Columbia's $2.2 billion budget for fiscal 1984 yesterday and gave the city $31 million more in federal money than it had requested, primarily for improvements in the D.C. detention system.

The additional money for improvements in the city's correctional system includes funds to ease overcrowding at the D.C. jail and to upgrade inmate training programs, among other initiatives.

The budget contains $493 million in federal funds, including a $386 million federal payment. In addition, the District received authority to borrow up to $115 million from the U.S. Treasury for capital improvement projects.

An additional $5.7 million in federal funds was put into the budget by a conference committee to bail out financially strapped St. Elizabeths Hospital, but Rep. Julian Dixon (D-Calif.), chairman of the House D.C. appropriations subcommittee, repeated on the House floor yesterday that this is the last time such aid for the hospital will be provided by Congress.

In other District-related activities on Capitol Hill yesterday, maneuvering continued around a bill designed to safeguard the city's home rule powers. Congressional sources questioned whether an effort would be made to include in the House version of the bill compromise provisions worked out Thursday by City Council Chairman David A. Clarke and aides to Mayor Marion Barry.

The provision is strongly backed by Clarke and deals with the council's power to pass resolutions of approval or disapproval of mayoral decisions.

The House District Committee struck the section on the power of council resolutions from the House version of the bill Wednesday after Rep. Stan Parris (R-Va.) objected to it.

Yesterday, a Parris spokesman said that Parris would vote for the compromise worked out by Clarke and Barry aides if it is introduced. But the spokesman said Parris will not ask for the compromise to be put in the bill, and said that Rep. Ronald V. Dellums (D-Calif.), chairman of the House District Committee, has told Parris he also does not intend to ask for it to be included when the bill comes up for a vote, possibly next Tuesday.

A Dellums aide said it is too early to say what Dellums will do. He said he was not sure Dellums had decided on the compromise.

The Dellums aide noted that the compromise was requested by Sen. Thomas Eagleton (D-Mo.) Wedneday, after Barry aides at the last minute withdrew their support for the original section of the home rule bill dealing with the council's resolution powers.

City Administrator Thomas M. Downs and Clarke agreed on the compromise lanaguage late Wednesday and signed a letter that was sent to Eagleton yesterday.

An aide to Eagleton said yesterday that Eagleton had not yet seen the letter, but that he can be expected to abide by any compromise worked out by Clarke and Downs.

Clarke spent part of yesterday lobbying for the compromise on Capitol Hill. A source close to the situation said he believes the easiest solution is for the compromise measure to be introduced in the House.

Pauline Schneider, Barry's director of intergovernmental relations, said yesterday that the Barry administration does not intend to ask anyone in the House to include the compromise language.

Asked if the Barry administration is working against having the compromise language included in the House version of the bill, Schneider said: "I can't commment on that."

Schneider then added: "I don't think we're working for it or against it on the House side."

The home rule protection bill was introduced as part of an effort to protect the city's self-government powers from possible court challenges that might arise from a recent Supreme Court ruling declaring legislative vetos unconstitutional.

However, the Federation of Citizens Associations of the District of Columbia argues that the Supreme Court ruling does not apply to the Home Rule Act because congressional disapproval of District bills is not a legislative veto.

Federation President Stephen A. Koczak said the group also opposes the bill because it would give the president the right to approve or disapprove District legislation--a power that is now confined to Congress once the mayor and council approve a proposed law.