Rep. Julian C. Dixon (D-Calif.), chairman of the House Appropriations subcommittee on the District, said yesterday he favors construction of a new prison in the city and will support federal funding for it.

"I would support a new prison facility. I am convinced there is a great deal of overcrowding" in the city's prison system, Dixon said in a brief interview following an afternoon of continued hearings on the District's fiscal 1986 budget.

"I have no problem supporting federal funding" to build it, he said.

Prospects for construction of a new District prison have been enhanced in recent months as overcrowding continues at the city jail in Southeast Washington and Lorton Reformatory in Fairfax County, and the D.C. prison population is expected to rise.

Sen. Arlen Specter (R-Pa.), chairman of the Senate Appropriations subcommittee on the District, started a push for a new D.C. prison last year to help relieve the overcrowding.

After strongly opposing construction of new prison facilities, Mayor Marion Barry reversed himself this year and said he could support one if it could be built on federal land with federal funds.

Barry plans to create a commission to determine what type of facility is needed and to find an appropriate site for it.

Specter is expected to add federal funds to the District's budget to pay for design of the new prison or the design and construction of the facility. Congress must approve the city's budget.

As subcommittee chairman, Dixon has a lot of power over the city's budget in the House-Senate conference and in the full House.

On another topic discussed at yesterday's subcommittee hearing, Rep. Frank Wolf (R-Va.) said he would circulate a letter to all 435 House members asking them to endorse a baseball team for Washington.

The city created a baseball commission to push for a team, and City Council member Frank Smith (D-Ward 1) said the District is pinning its hopes on getting selected for a National League expansion team if baseball team owners approve the addition of two teams at a meeting in August.

Washington is competing with six or seven other cities for a team. The District is trying to get Robert F. Kennedy Memorial Stadium transferred from the U.S. Interior Department to the city and plans a major renovation to get it ready for baseball. The city also is trying to get commitments for season tickets to show owners support for a team.

Dixon said he would support a team for Washington, even though he himself is not much of a baseball fan.