The Democratic National Committee is sending out letters to 1.5 million of President Carter's closest "friends" on phony White House stationery.

The letters look and sound like the real thing. But the stationery they are written on and the words on them aren't the president's.

The Democratic National Committee bought cheap paper and prettied it up so it looks like White House stationery. It wrote the letters -- although Carter approved the wording -- and mailed them out to 1.5 million names, culled from various magazine subscription lists.

It all was a fund-raising gimmick. "It seemed like the right thing to do. It's accurate to say the letter was from the president and he lives in the White House" said Trish Segall, direct mail manager at the DNC. "A lot of things people get in the mail, they automatically throw away. We thought people might at least open something from the White House."

They did. And a lot of them were outraged when they read the president wanted them to join something called "the President's Club." All they had to do was check a box saying they wanted to give from $10 to $25 to the Democratic Party.

One of them was House Republican leader John Rhodes (R-Ariz.). His letter was addressed simply: John Rhodes, Office Building, Washington, D.C.

Like the other letters, it began: "Dear Friend, I want to take a moment from the hectic pace of the Oval Office to bring you up to-date on the progress of our administration and to ask you to become a contributor to the Democratic Party."

Rhodes toyed with the idea of sending a letter back to Carter asking him to join the American Taxpayers Club, according to his press secretary, Jerry Lipson. He could do so by checking a box that would commit himself to "a real tax cut," or "a coherent energy policy."

The House minority leader has had trouble with White House mail before. One of the first letters the congressman received from Carter after he took office was addressed to "Dear Senator Rhodes."

When he received the fund-raising letter last week, "he just laughed," said Lipson.

The Carter letter was written by a professional fund-raiser, then forwarded to the White House for approval, said Segall of the DNC. "All the president did was make six or seven grammatical changes."

The letter he approved was a selfserving one that painted a rosy picture of the Carter presidency. It says, for example: "We've succeeded in cutting unemployment... we're getting control of runaway government.. we have cut spending and reduced waste.. we're facing up to inflation now."

It ends with a plea to join the President's Club, "an organization we have established to provide the financial strength necessary to insure the future of the Democratic Party."

According to Segall, the letter has been a overwhelming success, drawing about 83 percent more responses than the fund-raising appeals the chronically hard-pressed Democratic Party usually sends out.

There's apparently nothing illegal with using the phony White House stationery, provided it has a disclaimer on it, according to a spokesman for the Federal Election Commission. The letter contains a statement saying it is an appeal "sponsored" by the DNC, but nothing to indicate it didn't originate in the White House.

The President's Club is the least exclusive of three clubs the party sponsors for its financial backers. A $1,000 donation earns membership in "The President's Council": $5,000 gets membership in "The National Finance Council."

What does membership in the President's Club Club entitle a donor to?

"Our goodwill," said one DNC staff member. "It pays my salary."