Rep. Herbert E. Harris II (D-Va.) said yesterday that he would introduce legislation to provide about $800 million in federal matching funds that would be needed to complete construction of all planned 100 miles of the Metro subway.

Harris made his statement as he concluded two days of hearings on the status of the Metro construction program and problems it faces.

Metropolitan area officials testified yesterday that they are committed to completion of the system, but that they require federal help to do the job.

The most recent estimates show that the total Metro system would costs about $6 billion, or $1 billion more than the ceiling the federal Department of Transportation has placed on Metro construction.

Federal aid for mass transit projects is presently allocated on the basis of four federal dollars for each local dollar, or 80 percent federal. Thus $800 million would represent 80 percent of the needed $1 billion. The remaining 20 percent would have to come from local and state funds.

Harris said he would like to see a Metro authorization separate from other nationwide mass transit aid programs in recognition of the special relationship the federal government has with the metropolitan area.

There is no Metro contruction money in the current federal budget proposal now making its way through Congress. But Carter administration officials have said they are prepared to ask for $275 million for fiscal 1979 after Metro completes on a financial plan detailing sources of revenue for building and operating the system.

Harris said his legislation also would await completion of the financial plan, when more precise cost estimates and construction staging schedules will be available. The plan is due from the Metro Board by the end of August.

Harris also said he supports and would seek federal assistance for the costs of operating the subway that exceed fares collected. All the local officials who testified yesterday supported local taxes other than property taxes to pay the Metro deficit.