The man from Tass had a surprise for White House spokesman Marlin Fitzwater yesterday as he was completing his last formal daily briefing of the week.

Fitzwater had given out President Reagan's schedule when Nikolai Turkatenko had a statement and a question. Turkatenko, the bureau chief for the Soviet news agency, announced that Reagan had sent a letter "two or three days ago" to Soviet leader Mikhail Gorbachev.

"I thought maybe in the White House they have more glasnost," said Turkatenko, using the Soviet word for openness or publicity that has been associated with Gorbachev's policies. "Maybe you can tell us about it."

"I'll have to check this out," said Fitzwater.

American reporters then commented that the Tass bureau chief appeared to know more than Fitzwater did. "That's true," the spokesman said, with a nod to Turkatenko. "This man is amazing."

Fitzwater subsequently told reporters that the message from Reagan to Gorbachev had nothing to do with arms control negotiations between the two superpowers. Instead, he said, the message was one of four diplomatic cables that Reagan had sent to leaders of the permanent members of the United Nations Security Council asking them to support two pending U.N. resolutions calling for a cease-fire in the Iran-Iraq war and sanctions against any nation that did not abide by it.

Snappy Rejoinder . . .

An hour before Reagan announced that Robert H. Bork was his choice for the Supreme Court, First Lady Nancy Reagan stopped to chat with reporters in a White House corridor and was jokingly asked whether she had been responsible for the nomination.

"No," she quipped in reply. "I've been too busy with arms control."

June Achievements . . .

On the Hill, June was a great month for proclamations. Two winners were National Catfish Day and National Dairy Goat Awareness Week, and Congress' rush to proclaim hasn't gone unnoticed in parts of the White House.

The 100th Congress has sent 75 bills to President Reagan so far, and 38 of them have been proclamations.

The White House executive clerk's office notes that in its two years, the 95th Congress passed 633 laws, 20 of them proclamations.

Presidential special assistant and director of correspondence Anne Higgins said that congressional language in proclamations sometimes gets "changed in the staffing process," which was what happened to last month's National Fishing Week declaration.

Contrary to an item here poking gentle fun at a draft that promised surcease from the perils of drug abuse, the final proclamation simply salutes "the role of fishing in the lives of Americans."

Still, putting out dignified documents on animal topics is a strain. On June 25, the president celebrated catfish, observing that "farm-raised catfish have come a long way from their bottom-feeding ancestors."