Transportation Secretary Brock Adams' offer to help the Washington regional Metro system does not solve its most immediate problem - the lack of money to meet a $12 million interest payment due July 1, Metro general manager Theodore Lutz said yesterday.

Adams' letter also enraged Montgomery County Executive James Gleason because, in effect, it ordered a new study of whether to build a 4.5-mile subway line from Silver Spring through Wheaton to Glenmont.

"We just cannot survive in this county without that line," Gleason said, "and I intend to fight very hard for it."

But on the whole, most regional politicians and transportation officials interviewed seemed generally pleased that the Carter administration is taking an active role in dealing with Metro's financial difficulties.

In his letter to top regional transportation officials, Adams said that the Department of Transportation would pay $29 million in interest due on Metro revenue bonds in fiscal 1978, but that the $12 million payment due this July will have to be met by Metro.

"We just don't have $12 million lying around here," Lutz said yesterday. "Every dollar we've got is tied up in a legally binding interim agreement" to build 60 miles of the planned 100-mile subway. To meet the interest payment from existing metro money, Lutz said, would topple the delicately negotiated interim agreement.

Lutz met yesterday afternoon with Mortimer L. Downey, deputy under secretary of transportation, to explain the $12 million problem. "We'll have to be convinced that the money is not there before looking elsewhere," Downey said after the meeting.

If the $12 million payment is not met, Metro would be technically in default on the bonds, which are federally guadanteed. Metro officials have been seeking a federal commitment to pay 80 per cent. Originally, fares from the subway were supposed to pay both interest and principal on the $1 billion bonds that have been sold.

The restudy of the Glenmont line will throw a monkey wrench in the current schedule to decide how much of Metro will be built and how it will be paid for, accodding to George Wickstrom, who is directing a study of uncompleted Metro lines.

Four planned subway routes are currently under study. They run from downtown to Greenbelt, from downtown through Anacostia to Branch Avenue in Prince George's County near the Beltway, from Alexandria to Springfield, and from Glebe Road in Arlington along the Interstate 66 corridor to Vienna.

Those studies are scheduled to be completed in September, with local decisions based on the studies scheduled for the following spring.

"The region and its local officials have always had complete control over alternatives and their selection," said Wickstrom. "I think that's the reason we're as far as we are." The addition of the Glenmont route to the study, virtually by federal order, "makes the situation less palatable," he said.

Gleason was angrier. "What does Adams expect? Bus lines down Georgia Avenue?" Montgomery County, he pointed out, has eliminated two freeways inside the Beltway on the assumption the Glenmont subway would serve the Georgia Avenue corridor.

In addition to offering help on the revenue bonds for one year and requesting the study of the Glenmont route, Adams also said he wanted a long-range solution to Metro's financial difficulties, including both construction and operating costs.

"I welcome that portion of the letter," said Metro board member Joseph Wholey. "A crucial question to me is how much will be paid by the rider, how much by the real estate tax, and how much by some sort of regional tax." Wholey is also chairman of the Arlington County Board.

More and more local officials are talking about the need for some kind of regional tax to pay for Metro. To study that issue, the Montgomery and Prince George's councils decided late Thursday night to set up a joint committee to prepar a suburban Maryland position on the subject.