A major hurdle to completion of the full Metro rail system was cleared last night when Congress authorized $1.7 billion to build the last 40 miles of the 101-mile system.

Metro general manager Richard S. Page said "with this pledge from the federal government, the track is clear for construction of the remainder of the system," now scheduled for full operation in 1990.

Still needed, under terms of the federal authorization, are pledges by local jurisdictions that they will provide a "stable and reliable source" for the 20 percent of construction funds each is to furnish.

Final action in Congress came at 7 p.m. yesterday when the House, on a voice vote, agreed to go along with the Senate version of the legislation, passed earlier in the day, 66 to 23. The Senate eliminated $197.7 million in operating funds that were in the package passed by the House last July.

Rep. Herbert E. Harris II (D-Va.), cosponsor of the bill, convinced Metro supporters in the House to adopt the Senate proposal, rather than to seek a compromise on the subsidy, so that the measure could be sent to the White House before Congress recessed for the year. Harris said he would come back another time to seek an additional operating subsidy.

The House concurred with the Senate with little debate, although one opponent, Rep. Del Latta (R-Ohio) noted that the amount of the authorization was $200 million more than Congress was authorizing to bail out the financially troubled Chrysler Corp.

All four Washington area senators voted for passage. Sen. Charles McC. Mathias (R-Md.) told his colleagues it was "urgent to act now" so that the legislatures of Virginia and Maryland, which convene in January for only a few months, can meet the Sept. 3, 1980, deadline for assuring matching funds.The D.C. City Council, which also must meet that deadline, has pledged that it will earmark a tax to provide its share.

The only opposition voiced during the 45-minute debate yesterday came from Sen. Thomas F. Eagleton (D-Mo.), who said the legislation was "a bit too generous." He noted that while the federal government has poured billions of dollars into the Washington area transit system, the bus companies of St. Louis and Kansas City have received only $124 million combined in federal funds in the last five years.

Other big-city spokesmen disagreed, however. Sen. Carl Levin (D-Mich.) argued that, "It will not help Detroit and others to deny these funds. Quite the opposite, because this will take the pressure off other funds for which we all are competing" from the Urban Mass Transportation Administration.

Sens. John W. Warner (R-Va.) and Paul S. Sarbanes (D-Md.) also spoke in favor of passage and collared their colleagues as they entered the chamber and solicited their votes.

The area's fourth senator, Harry F. Byrd Jr. (I-Va.), also voted for passage. Byrd said after the vote that he had been unable to speak beforehand because he was participating as a conferee on the windfall profits tax legislation.

Byrd, one of the Senate's staunchest fiscal conservatives, said he voted for the bill because he favors "completion of the system as part of a commitment to states and localities." He called Metro "an important part of the government's transportation system."

Warner singled out Harris for praise, for cosponsoring the legislation with Rep. Fortney H. (Pete) Stark (D-Cal.). The House passed its more generous version in July by a vote of 261 to 125.

Harris sat on the GOP side of the Senate chamber during yesterday's debate, in which Warner called the liberal Democrat from Fairfax "a pioneer" who played "a particular leadership role in this legislation."

The $1.7 billion authorized would be paid to Metro by the U.S. Department of Transportation, beginning with $200 million in fiscal 1982, followed by $350 million in 1983, $375 million in both 1984 and 1985, $325 million in 1986, and $75 million 1987.