Mayor Marion Barry has asked the D.C. City Council to grant a 5 percent cost-of-living increase in benefits for about 34,000 families on welfare, effective Feb. 1.

The proposed increase would cost the city government an additional $3 million a year and would apply to recipients of Aid to Families with Dependent Children (AFDC) and public assistance.

Funds to cover the proposed increase were included in the fiscal 1982 budget approved by Congress, according to a spokesman for the mayor.

City Council Chairman Arrington Dixon said yesterday that the council would probably act on the proposal next week at a special session. "It will be a nice Christmas present," Dixon said.

The council also will consider a plan to bring the city's AFDC program into compliance with new, more restrictive federal welfare guidelines. Barry and officials of the U.S. Department of Health & Human Services have raised technical objections to the proposal.

If the cost-of-living increase is approved, a family of four with a maximum monthly income of $715 would be entitled to $366 in welfare benefits, while a family of eight with a maximum monthly income of $1,230 would receive $630 in benefits.