The House of Representatives approved the District of Columbia's $2 billion fiscal 1984 budget yesterday by a vote of 296 to 124, with no attempts made to amend the bill as passed by the House Appropriations Committee.

Rep. Julian C. Dixon (D-Calif.), chairman of the Appropriations subcommittee for the District, said there were some areas of concern in the budget, including a sharp reduction in the number of District employes. The 31,913 positions in the budget reflect an 18.4 percent decline from fiscal 1980, when there were 7,192 more positions, he said.

One potential problem is a $25 million funding gap for St. Elizabeths Hospital between what costs are expected to be and what is provided in the city and federal budgets. Dixon said he hoped the issue would be resolved by the time the bill gets to conference with the Senate.

The bill differs from the budget as approved by the D.C. City Council in several ways. It requires the city to continue to pay the Potomac Electric Power Co. for street lighting and traffic signals until it is determined whether the District will succeed in transferring the cost to Pepco and ultimately the utility's ratepayers.

It requires the city to pay off $20 million of its accumulated general fund deficit, rather than $5 million as the District had planned. The long-term deficit is expected to be $256 million at the end of 1984.

The Senate has not yet acted on the budget.