The Carter administration has lifted its opposition to the $1.7 billion Metro construction bill pending in Congress, removing a major obstacle to completion of the full 101-mile rapid rail system.

The House passed the proposal overwhelmingly in July despite the last minute active opposition of the White House. A source said last night the policy change by the administration would smooth the way for approval in the Senate, where White House opposition and the threat of a veto could have at least delayed the proposal.

Rep. Herbert E. Harris II (D-Va.), a cosponsor of the legislation, said yesterday the reversal is "great news for Metro." The administration will continue to oppose a provision in the bill that would authorize a $197.7 million federal operating subsidy.

A White House spokeswoman confirmed last night that an agreement was reached with Metro officials. She said Assistant Transportation Secretary Mortimer L. Downey will testify in behalf of the bill on Friday before Sen. Thomas D. Eagleton (D-Mo.), chairman of the Senate D.C. appropriations subcommittee.

The bill guarantees an 80 percent federal share of the cost of building the last 40 miles of the system -- up to $1.7 billion. The system is scheduled for completion by 1987.

Early action on the bill is important because of a requirement in it that a "stable and reliable source" of the 20 percent local share be in place before any federal funds are released. Those assurances most likely would result from actions by the part-time legislatures of Maryland and Virginia, which meet beginning in January, and the D.C. City Council.

The federal concern over the reliability of local funds arises because Metro lacks taxing authority. Its deficits are made up by local governments, who technically have no legal obligation to support the system. Most of the burden has fallen on local property taxes. In Virginia, for example, Gov. John Dalton and the legislature have been reluctant to appropriate money for construction and also have refused to allow Northern Virginia suburbs to add a penny to the sales tax, as is often proposed.

Among the factors credited by Harris with helping reverse the White House policy were the energy crisis and the lopsided House vote of 261 to 125 approving the bill in July.

Harris refused to concede that the operating subsidy would be lost in an inevitable compromise between the House and Senate versions. He said federal support of construction costs "assures completion of Metro and that is the fundamental purpose of the bill," which was cosponsored by Rep. Fortney H. (Pete) Stark (D-Calif.).