D.C. Mayor Marion Barry has proposed designating $2.2 million in city transportation funds to complete work on the long-unfinished quarter-mile segment of Rte. I-395 between E Street NW and New York Avenue NW.

The money would be used for paving, electrical and tile work in a 1,200-foot tunnel beneath Massachusetts Avenue NW. Other work on the segment was finished long ago, but officials have never been able to find the money to complete the project. For the last decade part of the section has been used as a parking lot.

Barry proposes to finance the project by shifting surplus money from a number of city road projects that have been completed for less than the expected cost, according to Transportation Department officials.

The completed segment would link the Southwest Freeway to New York Avenue, allowing motorists to bypass several stoplights on Second and Third Streets NW, which are now much more congested than they were ever designed to be, transportation officials said.

The unfinished segment is part of what planners designated as the Center Leg of the Inner Loop Freeway, once proposed as an elaborate system of highways linking the city's inner core with the suburbs. Other segments of that system were eliminated when city officials decided to transfer funding for them to the Metro rail system. The Center Leg runs north-south under the Mall and parallel to Second and Third Streets.

Congressional opposition to the project as a line-item in the city budget and other priorities among city road planners have kept the city from finishing the segment sooner.

Barry's proposal to shift funds to this project has been forwarded to D.C. City Council members, who have until tonight to lodge any objections. None are expected, according to council staff members.

After council clearance, the request must be approved by Congress.

The city money would be matched with about $18 million in federal highway funds to meet the expected $20 million cost of the project. Federal money is regularly allocated for interstate highway projects in the city, but has not been used to finish the Center Leg because the city has not come up with the required 10 percent of the total cost.

Federal highway officials said yesterday that if the city came up with the money, there would be no problem designating federal funds to complete the project.

If the project receives congressional approval, work could begin by the end of the year, and the project would be completed in about two years, city officials said.