Metro officials asked Congress yesterday to give them nearly 50 percent more in federal funding than President Reagan has budgeted for fiscal 1984, warning that without the extra money, openings of several stations on the subway system's priority lines could be delayed for years.

The administration had requested $305 million for fiscal 1984, $46 million less than for fiscal 1983. At a hearing of the Senate Appropriations transportation subcommittee yesterday, Metro General Manager Richard Page asked that Congress instead provide $454 million.

Subway construction plans already have been delayed by reductions in the 1982 and 1983 budgets and further cuts "would not only cause major delays but make it extremely difficult to sustain the fragile political coalition" of the local jurisdictions that provide 20 percent in matching funds for the subway system, Page said.

"If construction is postponed far into the future, costs will be considerably more, completion will seem unlikely or remote and the political glue will begin to crack," he said.

Page and subcommittee Chairman Mark Andrews (R-N.D.) also ridiculed the administration's assumption that $20 million of the funds it budgeted could be found from unidentified "other sources."

"Do you believe in magic?" Andrews asked Page.

"This authority has been held together by a little bit of everything, including some magic, but this is a new one," Page replied.

After the hearing, Page said he was "encouraged" by the subcommittee chairman's expression of concern over the administration's numbers. While he had received no commitment from the subcommittee for an increase in funding, he had not expected one yesterday, Page said.

The $230 million in identified construction funds in the Reagan budget would be inadequate, causing "major disruption to our program, our schedule and our costs," Page said.

Specifically, it would delay completion of stations on the Orange Line to Vienna from 1986 to 1987, on the Red Line to Wheaton from 1989 to 1990 and on the Inner Green Line from Anacostia to U Street from 1989 to 1991, he said.

The Shady Grove station will not be able to open until late 1984, a year's delay from earlier plans, even though the track has been completed, Page told Andrews. This is because Metro will not have enough subway cars to operate to the station until then, because a strike at a Pittsburgh air brake plant last year delayed the manufacturing of the cars in Italy.

The administration's budget request of $6 million in operating subsidies, a $13.5 million cut from fiscal 1983, would have to entail cutting service, raising fares or increasing the cost of the system to local governments, Page added.