A group of prominent District, Maryland and Virginia officials plans to launch a lobbying campaign today to persuade Congress to overturn the Reagan administration's budget-cutting recommendations and provide additional federal funds to expand the Metro subway system.

President Reagan has recommended cutting off all spending for Metro construction after the current fiscal year, which ends Sept. 30. The cutoff threatens to stall Metro's plans to extend the 60.5-mile rail system to 89.5 miles by the early 1990s.

The officials, headed by D.C. City Council member Polly Shackleton (D-Ward 3), will announce the campaign on the Capitol steps today. D.C. Mayor Marion Barry and Maryland Gov. Harry R. Hughes are expected to attend, officials said, and Virginia Gov. Gerald L. Baliles has been invited.

The group, called Friends of Metro, also includes former Transportation secretary William T. Coleman Jr.; former Virginia governor Charles S. Robb; Peter F. O'Malley, a Prince George's County lawyer and president of the Greater Washington Board of Trade; R. Robert Linowes, a lawyer and civic leader, and Luther H. Hodges Jr., chairman of Washington Bancorporation, which owns the National Bank of Washington.

"What is really important is to be able to finish the Green Line," said Shackleton. "It's crucial that we do it and that we finish up the system."

The Green Line, Metro's only unopened subway route, is designed to serve low-income District neighborhoods, such as Anacostia, and major areas of Prince George's. Also jeopardized by Metro's shortage of funds are a Red Line extension in Montgomery County and a Yellow Line branch in Virginia.

Key members of the House Appropriations Committee recently said they would attempt to allocate funds for Metro construction next year, but no figure was cited. Under a Senate budget plan, Metro would be allotted $217.2 million next year, the same as the current appropriation.

The Metro system, which recently stepped up its own lobbying, is seeking about $250 million in federal funds annually for the next three years. A spokesman said Friends of Metro will be privately financed.