The Reagan administration yesterday told a Senate panel it "strongly supports" the city's plans to help solve its budget problems by selling $184 million in bonds, while a key House committee approved legislation authorizing the bond sale.

"As a matter of principle, the administration believes that the District should be managing its own finances," Assistant Treasury Secretary Roger W. Mehle told the Senate subcommittee on Governmental Efficiency and the District of Columbia. "In sum, the decision on the financing strategy should be made by the District, and the decision on the success of a bond sale by the marketplace."

Meanwhile, the House District Committee approved the bonding legislation, the key element in Mayor Marion Barry's financially and politically important fiscal rescue plan. At the same time, Rep. Stewart B. McKinney (R-Conn.), ranking minority member of the panel and a one-time foe of the measure, said he will not try to block the bill when it reaches the floor of the House.

The House committee vote means that the bill could reach the floor of the House by the end of the month, although there was no indication yesterday when the Senate might act. Phillip C. Dearborn, financial adviser to Barry, said the city could begin selling the bonds in the private market within three to four months after final congressional approval.

While the administration's support does not ensure passage of the bonding bill, city officials believe that without it, the measure would have had little chance. The D.C. officials said they believe the administration's support will help persuade conservative Republicans to vote for the bill.

The legislation had been bottled up in committee on both sides of the Hill, while some congressmen, including McKinney, argued that it was unwise for the city to finance a deficit in its operating budget with long-term borrowing. The accepted practice in most cities is to use such borrowing only to finance capital projects, such as major construction efforts. b

But a Treasury spokesman said the Reagan administration has been working quietly for the last several weeks to convince skeptics like McKinney that the city, and not Congress or the White House, should decide whether such borrowing is appropriated in this case. He said the administration plans to continue lobbying for the measure in both houses of Congress.

The administration earlier imposed limits on the city's right to borrow from the U.S. Treasury, but does not oppose the city in its efforts to borrow in the private market because most other local governments in the U.S. already do so.

The bonding legislation is important to Barry, who is expected to seek reelection, because it would enable him to eliminate the deficit without resorting to politically costly tax increases or cutbacks in city services and layoffs of government workers.

Barry attempted to make the bonding bill easier for skeptics on the Senate subcommittee to swallow by suggesting that it be amended to specify that the federal government will not be liable should the city default on the bonds.

When that amendment was proposed on the House side, some committee members remained unconvinced, contending that in the final analysis the federal government would remain responsible for a city default. But only one Republican member of the panel, Rep. Thomas J. Bliley Jr. (R-Va.), said he remains convinced that the city should not be allowed to sell the bonds. Bliley and three other Republicans abstained when the committee voted 7 to 1 to approve the measure. But Bliley said he plans to send a minority report to the floor expressing his concerns.

"I am concerned that the District has not taken the actions necessary to balance its budget this year and in coming years," Bliley said.

Committee Chairman Ronald V. Dellums (D-Calif.) said the city's projection last week of a $7-million surplus for the fiscal year ending Sept. 30 "clears up any question of the city's ability to keep its expenditures under control."

In another D.C. financial development, the city school board failed to persuade Barry to avert furloughs for teachers and other school employes by giving the school system $4.8 million of the surplus. Replying for the mayor, budget director Gladys W. Mack said such a rescue operation would be illegal because it would allow the school system to spend more than the amount authorized by Congress.

D.C. School Superintendent Floretta D. McKenzie said that without the use of the surplus money teachers will have to be furloughed for six days and other school employes for four days without pay before classes resume in September, thus saving $3.8 million. Another $1 million can be saved by delaying school maintenance and purchase of supplies, she said.

Meanwhile, the City Council yesterday approved Barry's revised spending plan for fiscal year 1982, even though the budget amendment does not include enough money to fully fund the city's pension liability or pay raises for city workers.

Dixon said he received assurances from the mayor that as soon as Congress approves an additional $36 million federal payment to the city, that the money will go immediately into the pension fund and help pay for the salary increases.