The cash-hungry U.S. Postal Service agreed yesterday to spend $15.4 million to provide a new home for the nation's stamp collection.

Under an agreement approved by a 7-3 vote of the Postal Service's board of governors, the service agreed to transform a portion of Washington's old main post office at Massachusetts Avenue and North Capitol Street NE into a museum that will house the National Philatelic Collection.

The collection, which contains many of the world's rarest stamps and postal exhibits, has been a part of the Smithsonian Institution since 1911 when the old Post Office Department gave up on its plans to operate a separate museum in Washington. Smithsonian officials said they have never placed a dollar value on the collection, which nonetheless is considered one of the most valuable in the museum system. There are 16 million items in the collection, most of them stamps.

Postal officials were quick to note yesterday that funds for the new museum would come not from mail users, but from an international stamp show the Postal Service plans to host at an unspecified city sometime in 1994. As a result, Al DeSarro, a postal spokesman, said the museum's costs will have "nothing ... whatsoever" to do with the service's pending request for higher postage rates.

The service, which yesterday projected its fiscal 1990 losses at $850 million, hopes to receive permission early next year to boost the postage of a first-class letter from 25 cents to 30 cents to meet its operating deficit.

Postmaster General Anthony M. Frank noted in a statement that the Postal Service financed a conference of world postal leaders in Washington last year with the proceeds of a "highly successful" stamp exhibition. Even so, three members of the postal board of governors dissented from the museum plan, saying that the service, which is in the midst of wage negotiations with its powerful unions and a billion-dollar automation effort, could better spend the money on other projects.

Smithsonian officials expressed delight with the agreement, saying it would give greater exposure to the stamp collection, which, despite its worldwide reputation, gets relatively little space and attention in its current third-floor location in the National Museum of American History on the Mall.

"I think the size of it will be to our advantage," said Herbert Collins, executive director of the stamp collection, noting that it will have 76,000 square feet of space, compared with 8,630 square feet in the American History Museum. "Here's a place where visitors can spend a couple of hours and see it end to end," he said.

The collection contains scores of rare stamp errors, including the 1918 inverted biplane airmail stamp, considered perhaps the best known stamp misprint in U.S. history. It also contains some bigger items, including Benjamin Franklin's 1770s post office ledger, the first Highway Post Office bus and several early mail planes -- far more than can be exhibited in the current space.

"This stamp collector thinks it's terrific," said Michael Laurence, editor of Linn's Stamp News, the country's largest philatelic publication. "I've been down on the Smithsonian for some time. They must have the good stuff in back vaults somewhere but what they show is pathetic. This is an opportunity for stamp collectors."

Under the agreement with the Smithsonian, the Postal Service will pay for the larger quarters in the old post office building, which is currently being remodeled by the Postal Service and a private developer. In addition, the service will guarantee $2 million of the museum's expected $3 million a year operating costs with sales of philatelic items. The Smithsonian will provide the other $1 million.

The new museum, which would be the first in the city to be operated jointly by the Smithsonian and another government agency, is Collins's brainchild. He said yesterday that he got the idea during a 1982 visit to Ottawa, where he inspected a museum operated jointly by the Canadian government and the country's postal system.

Collins quickly sold the idea to Postmaster General William F. Bolger, and after he left office in 1985 Collins kept pressing the idea on Bolger's successors. The Smithsonian's board of regents gave its approval to the concept several years ago, a spokeswoman said.

The new facility could be open to the public as early as late 1993. The staff of 11 workers who maintain the collection at the Smithsonian will grow to 69 with the addition of security and maintenance personnel. It would be operated as a branch of the American History Museum, where the collection has been housed since 1964.

The remainder of the post office building is being remodeled by a private firm at a cost of $193 million. A new postal station will be placed in the building and the other spaces probably will be rented to other government agencies, DeSarro said.