Both houses of Congress and President Carter acted swiftly yesterday to provide stopgap financing that will assure fully pay for 243,000 employees of the Health Education and Welfare and the Labor departments, and avert a financial crisis for the District of Columbia.

The lawmakers enacted, and the President promptly signed, a so-called "continuing resolution" permitting the three governmental units to spend until Oct. 31 at the same level as the last fiscal year, which ended Sept. 30.

All three units have limped along financially for the past 13 days, bringing anguish to employees threatened with a pay curtailment or cutoff and uncertainty about departmental and municipal functions.

Yesterday's action gives another two weeks for joint House-enate confernece committees to reach agreements on the regular Labor-HEW appropiration bill and the D.C. budget for the 1978 fiscal year.

The Labor-HEW bill is stalemated by a dispute over federally financed abortions, and the D.C. budget over a proposed convention center.

As approved, the continuing resolution also will permit the issuance of paychecks to 4.178 employees of the Agency for International Development, including 2,800 at its Washington headquarters. Other AID spending still is frozen in a congressional dispute over World Bank financing.

Enactment of the financing resolution should assure full, normal pay next week for HEW employees, but it came too late for the Labor Department.

A Labor spokesman said half-pay checks, for work done before Sept. 30, already have been mailed. But he said there is good news, too: checks for the other half of the pay period, since Oct. 1, will be mailed over the week end.

"I'm glad. I hope it's for real," Shirley Wilson, a Labor Department clerk-typist, said when told the news. "Now I can eat."

The D.C. government maintained normal operations during the money freeze, and apparently planned to pay $8 million to 16,500 of its employees next Tuesday. A spokesman for the Treasury Department, which acts as the District's banker, said the department would have insisted on certification that funds to meet the payroll had been legally appropriated by Congress.

Until yesterday, House leaders had resisted passage of a continuing resolution, hoping its lack would keep pressure on for settlement of the abortion issue and enactment of the Labor-HEW appropriation.

Customarily, when it decides on a continuing resolution, the House enacts a single measure dealing with all pending appropriation bills. Thus, without action on Labor-HEW, the District and AID funding also was sidetracked.

The Senate, feeling heat from U.S. workers threatened with payless pay-days, finally decided Wednesday to prod the House by enacting its own continuing resolutions - separate ones for Labor-HEW and for the District. That would have prevented the District from getting snarled in a possible side dipute over abortions if and when the measures reached the House floor.

House leaders ignored the Senate resolution yesterday, regarding it as s breach of congressional custom under which the House originates all appropriation measures.

Chairman George H. Mahon (D-Texas) of the House Appropriation Committee, with support from Speaker Thomas P. O'Neill (D-Mass.), drafted his own resolution and introduced it when the House convened at 10 a.m. yesterday.

Like the Senate version, Mahon's resolution preserves - for the two-week period - the tight restrictions on abortion financing that was in effect in the past fiscal year.

Seekin unanimous consent to bring the measure up for action immediately, Mahon was blocked by a protest from Rep. Fortney H. Stark (D-Calif.), a backer of liberalized abortion policy. Mahon promptly went to the Rules Committee, then in session up another matter, and got clearances for floor action.

Within minutes, and without controversy, the resolution was approved on a voice vote: "The purpose . . . is to enable people who work for the government, and who are entitled to be paid, to get their pay," Mahon explained.

Less than three hours later, the Senate Appropriations Committee met and, with barely a mention of rebuff of its own resolutions, approved the House version. It was enacted by the Senate literally as fast as Sen. Warren G. Magnuson (D-Wash.) could walk into the Senate chamber to call it up.

Meanwhile, the basic dispute on the abortion provision of the $60.1-billion Labor-HEW bill continued. The House, again insisting on its rigid anti-abortion stance, voted, 234 to 163, to reject a motion by Rep. Newton I, Steers Jr. (R-Md.) to accept the Senate's more permissive language.

Then the House asked for a new joint conference with the Senate to try again for an agreement.