D.C. Council members pressed city officials on Thursday to explain why spending has been frozen on key programs and why warnings of a quarter-billion­dollar budget gap loom less than a week after financial officials announced the District ended its last fiscal year well in the black.

Several lawmakers cited mixed messages about the state of the District’s finances, seen in three seemingly contradictory numbers: an estimated $240 million gap that must be closed in the 2016 budget; a projected $83 million revenue shortfall for the current fiscal year; and the $204 million budget surplus announced last Friday.

Mayor Muriel E. Bowser (D) has struck a note of fiscal caution in the opening weeks of her term, freezing some hiring, employee travel and a number of city programs. But council members who attended the Thursday hearing on the city’s 2014 fiscal performance said the prior year’s surplus undercut any talk of dire fiscal straits.

“Why would we continue to have a freeze on things that really matter?” said Elissa Silverman (I-At Large). “There’s a cognitive dissonance here. With all this money coming in, why are we not spending on the things people are consistently saying they care about?”

Those issues, Silverman and others said, include affordable housing and homelessness, which have been an area of focus for Bowser and the council alike. One line item frozen by Bowser is $600,000 to allow for the hiring of more social workers to assist homeless families.

Council Chairman Phil Mendelson (D) lectured City Administrator Rashad M. Young on Bowser’s handling of budgetary matters, arguing that the hiring freeze, routine underspending and an expected $21 million court settlement made the program cuts unnecessary.

“There’s an excess of caution, an unnecessary level of caution,” Mendelson said. “You have it within your control to control spending and ensure the budget that was balanced remains balanced. The freeze has been really obnoxious to the council.”

But Young said any decisions on which spending would be unfrozen would wait until new revenue estimates are released this month. “I think it’s important as we look at the list here that we understand what the challenge is or isn’t,” he said.

Chief Financial Officer Jeffrey S. DeWitt, who is independent of the mayor and council, said the fiscal contradictions have been driven by a confluence of slowing revenue growth and agency underspending.

While unanticipated revenue growth had driven massive surpluses in prior years, it was underspending, DeWitt said, that accounted for last year’s $204 million surplus. The 3.4 percent differential in expenditures was unusually high, he said, and could be explained by the long lame-duck period for then-Mayor Vincent C. Gray, in which some key staffers departed and there were delays in implementing some programs.

Meanwhile, the current and future gaps have been due to downward adjustments in revenue projections — particularly from capital­-gains income tax and traffic camera fines — and the rising costs of government, driven largely by increasing salary and health-care costs.

The 2014 surplus, now part of a reserve balance approaching $2 billion, is not available to cover future shortfalls unless a city law aimed at building the District’s cash holdings is changed.

DeWitt said he would present a more detailed report on the underspending in the coming days, and Young said mayoral budget officials are exploring whether agency spending targets could be readjusted to help close the budget gaps.

Several council members pressed Young to unfreeze a $5 million grant to the Washington Humane Society, which contracts with the District government to handle its animal control functions. The grant would help the nonprofit group acquire property near the Washington Navy Yard for a new headquarters to replace its facilities on New York Avenue NE and Georgia Avenue NW.

Jack Evans (D-Ward 2) and Mary M. Cheh (D-Ward 3) told Young that the deal’s closing is rapidly approaching and could be jeopardized if the funds aren’t unfrozen.

“There’s been no end to the problems over there,” Cheh said. “It’s not as if we can allow the animals to run amok.”