The Senate passed its version of the District of Columbia's $2 billion fiscal 1984 budget yesterday, including an additional $26.6 million earlier voted by its appropriations committee to ease overcrowding at the D.C. jail and to improve inmate training programs.

The House-passed version of the city's budget did not include those funds, and the differences will now be hashed out in a conference committee.

A knowledgeable House source said that House officials are likely to agree to give the embattled D.C. Corrections Department more money. House and Senate sources said an agreement could be reached in time for both houses to adopt the budget before their summer recess begins next week.

The $26.6 million added by the Senate also includes $2.8 million for seven new D.C. Superior Court judges and $1.5 million to study the controversial idea of a merit-pay system for city school teachers. The addition of the judges is aimed at helping reduce the backlog of criminal trials that is contributing to jail overcrowding.

Neither proposal was included in the House budget.

Under the Senate proposal, the bulk of the additional funds, $22.3 million, would go to the Corrections Department.

D.C. corrections director James F. Palmer told a Senate subcommittee yesterday that his department needs all the additional funds it can get.

Last weekend Palmer ordered the transfer of about 430 inmates from the D.C. jail to the Lorton Reformatory in Northern Virginia after inmates protesting overcrowding and other conditions staged two major disturbances.

The jail was built to house 1,355 prisoners, but its total population had been about 2,400 in recent months.

Largely as a result of the transfers to Lorton, the jail's population was down to 1,998 inmates yesterday, and Lorton was housing 3,282 prisoners, nearly 300 more than its capacity.

Responding to a question from Sen. Arlen Specter (R-Pa.), architect of the plan to give the department more money, Palmer said both the jail and Lorton are now "safe and secure." But, Palmer said, without infusion of more funds the potential remains for new inmate eruptions.

Palmer and other city officials have said further efforts to ease overcrowding at the jail center on plans to increase capacity at Lorton by 800 to 900 during the next year. Palmer has called Lorton the "most logical" place for expansion.

However, plans to increase the number of prisoners at Lorton have drawn strong protests from Northern Virginia politicians and residents, who have long sought unsuccessfully to have Lorton closed and a new prison built inside the District.

In addition to the planned increase at Lorton, the Senate added $2.5 million to provide 200 to 500 inmate spaces by converting to prisons surplus federal property in the District, possibly at St. Elizabeths Hospital or Bolling Air Force Base.

However, city officials said they have been unable to find any available federal property so far.

District Del. Walter E. Fauntroy, echoing a view held by other local elected officials, who opposes attempts to expand prison facilities in the District, has said he plans to ask for the money for the conversion of surplus property to be cut from the budget.