Daniel J. Terra, President Reagan's ambassador at large for cultural affairs, and founder of the Terra Museum of American Art in Evanston, Ill., has paid $3.25 million for "Gallery of the Louvre," a painting by 19th-century American artist-inventor Samuel F.B. Morse.

It is believed to be the highest price ever paid for a work of art by an American artist.

"It's a very important statement about cultural development in this country, but I never dreamed I'd own it," said Terra yesterday.

He bought the 6-by-9-foot painting from Syracuse University, which received it as a gift in 1884. Syracuse agreed to the sale, according to Terra, on the condition that the painting be made more accessible to the public.

"I've known about the painting since I read about it in the Britannica when I was in college," said Terra. "On my trips to Syracuse, I saw it in the library three or four times and expressed interest in it over the years. When I heard they were considering selling it, I called to ask that I be advised when the time came. They had a New York dealer, Coe Kerr, and I had a New York dealer, Berry-Hill Gallery, each advising us." He said negotiations with the university began in March and the deal was closed this month.

Considered one of Morse's masterpieces, "Gallery of the Louvre" was painted in the Louvre in 1832. It depicts several Americans viewing 38 paintings hanging in the museum's Salon Carree. Morse shows himself as teacher, leaning over a student's shoulder in the foreground; in the left corner are novelist James Fenimore Cooper, his wife and their daughter, who was an art student of Morse. Surrounding them are miniature reproductions of paintings by Rembrandt, Leonardo, Rubens, Raphael and Titian. The painting is in the tradition of earlier "gallery" pictures painted between the 17th and 19th centuries.

The record price for an American painting sold at auction is the $2.5 million paid for Frederic Church's "Icebergs" in October 1979, at Sotheby Parke Bernet. No similar records are kept of private sales, but several leading dealers in American art agree that this probably sets the record.

"I can't think of another American painting that comes close to that figure," says Robert Vose, 71, who has run his venerable Boston gallery for 50 years.

"To my knowledge, it is a record," agrees Lawrence Fleischmann of New York's Kennedy Galleries, one of the largest in the world devoted to American art. "But we ourselves have sold a Winslow Homer seascape for $2.5 million within the past two years. It used to be that $100,000 was the top, but now more and more we are crossing the million-dollar mark on American pictures."

A widely publicized pair of portraits of George and Martha Washington by Gilbert Stuart, now owned jointly by the National Portrait Gallery and the Boston Athenaeum, brought $4.87 million in 1980, but that was for two paintings.

"Gallery of the Louvre" was made 10 years after Morse's "The Old House of Representatives," now in the Corcoran Gallery of Art. Both were conceived as exhibition pieces that Morse hoped people would pay admission to see. Both failed to produce the expected income, leading Morse to refocus his attention on what had been an avocation in scientific research. He subsequently produced the telegraph and the Morse Code, which ultimately overshadowed his accomplishments in art.

Terra is a self-made multimillionaire and founder of Lawter International Inc., a chemical conglomerate; as finance chairman for Reagan's campaign, he raised $21 million. Terra owns other record-price paintings, including "The Jolly Flatboatmen" by George Caleb Bingham, which he bought at auction in 1978 for close to $1 million. He and his late wife, Adeline, began collecting American art in the early '50s, and in 1980 opened Evanston's Terra Museum of American Art. Terra recently acquired a prime corner on Michigan Avenue in Chicago, where his new museum is slated to be built to house this and other paintings in the Terra collection.

"This is an icon of American art," says Terra Museum curator David Sokol. "It's a very well-known painting, and appears in all kinds of standard histories of American art. It's an icon because it includes Morse the artist president of the National Academy of Design and his friend Cooper, dean of American novelists at that time within the Louvre, surrounded by all the great treasures of painting. It symbolizes the American inheritors taking over within the Old World citadel of culture."

From his Evanston museum office, Terra, 71, said, "We hope to begin showing the painting to the public on Aug. 15. I hope we can make it. It never got off the ground in the good old days when they wanted to put it on tour. Here we are 150 years later, and maybe we'll put it on tour and finally fulfill their plans."