D. C. Mayor Walter E. Washington asked a congressional committee yesterday for federal help in absorbing the city's unfunded pension liabilities, which he said have now topped a "staggering" $2 billion.

That figure, the major told a House District subcommittee, is $300 million greater than the "frightening level of $1.7 billion . . . we inherited" when home rule replaced the previous federally-dominated local government in 1975.

Since Congress enacted the costly pension programs into law more than a half century ago, Washington said, the federal government should relieve the city of much of the burden it imposed.

Washington, City Council Chairman Sterling Tucker and D. C. budget director Comer S. Coppie went to Capitol Hill to testify on a bill that would reform the pension program for city police officers, firefighters, public school teachers and judges. A similar bill was considered last year, but not enacted.

Pension payments for these retirees are included in each year's District of Columbia budget. The $2 billion cited by the mayor is the estimated total that the city and its taxpayers would have to pay over many years to both current and future retirees.

Other District employees and retirees are covered by U. S. . pension programs, with benefits paid from a fund to which the city contributes regularly.

The pending bill, sponsored by Rep. Romano L. Mazzali (D-Ky.), would create a pension fund and a 10-member retirement board to administer it.

Washington told the subcommittee, headed by Rep. Ronald V. Dellumus (D-Calif.), that the method proposed in the bill for calculating payments into the new pension fund would not make inroads into the existing $2 billion liability.

Copple testified that it would not be necessary to create a $2 billion fund in one bite.

A precedent exists, Coppie said, in the 1974 law that required the funding of pension programs by private industry over a period of 30 to 40 years. He suggested the District and federal government could make annual payments into a fund over similar period

The mayor objected to the creation lf an independent retirement board and to its proposed composition.

Under the bill, the board would have 10 members, eight of them representing city employees and retirees and two representing the District government.

Tucker, said that "the views of the city would not likely receive the type of attention necessary" under this arrangement.

Tucker suggested that the board, if created, be composed of equal representation of the affected employees and of the city government.

The mayor said he had been trying for six years to get support for a reform of the pension programs.

"We cannot afford to consider pension without coming to terms with the city's overall financial situation," the mayor testified.

"We have yet to exercise the authority granted us under home rule to sell District bonds on the municipal bond market," instead of borrowing from the U.S. Treasury, he added.

"When that time comes," he said, "we will have a far better opportunity to obtain favorable rates as we demonstrate to the investment community that positive action is being taken to reduce our unfunded pension liabilities."