Prime Minister Margaret Thatcher was described today as "very distressed" by the disappearance of her race-driver son, Mark, during a trans-African competition. She canceled a meeting with the visiting Hungarian foreign minister after breaking into tears en route to a public function this morning.

After days of confused reports, Mark Thatcher, 28, his French co-driver, Charlotte Verney, 38, and a mechanic, were officially listed as missing yesterday. Planes have been searching since Monday. The two were last seen Friday along a remote, unpaved and largely unmarked desert route through Algeria and neighboring Mali. The French-organized, 6,000-mile endurance drive from Paris terminates in Dakar, Senegal on the western coast of Africa.

The prime minister's husband Denis flew today to the Algerian desert town of Tamanrasset, 1,200 miles south of Algiers, where the search for his son is being coordinated by the rally organizers and the Algerian, Malian and French governments.

Another driver said Thatcher told him he had stopped to repair a cracked axle and hoped to rejoin the rally, according to the Thierry Sabine public relations firm in Paris that runs the 4-year-old rally. British diplomats in Algeria received conflicting, unconfirmed reports today that Thatcher's car, a white Peugeot 504, had been sighted since then in Algeria or Mali, but a spokeswoman for Thierry Sabine said tonight they have no reliable information on Thatcher's whereabouts.

British diplomats have complained about the paucity and unreliability of information from the organizers. About 180 of the 290 cars, jeeps, trucks and motorcycles that left Paris on New Year's Day have dropped out of the race so far, according to the spokeswoman in Paris. She also said a Dutch motorcyclist, a French journalist and Malian youth had been killed.

Several dropouts have been rescued from the desert, including one who apparently was mistaken for Thatcher at the weekend. The surviving entrants are expected in Dakar a week from today.

French President Francois Mitterrand expressed his concern in a personal message to Prime Minister Thatcher. His defense minister, Charles Hernu, ordered three French military aircraft to join the search.

Prime Minister Thatcher was red-eyed and visibly fighting back tears when asked about her son by reporters as she entered a London hotel this morning to address the British Federation of Self-Employed and Small Businessmen.

"I am sorry there is no news," she told them. "I am very concerned. My husband will arrive there this afternoon."

Inside the lobby, she began crying and had to be supported briefly by aides. Composing herself, she made her scheduled speech, answered questions about economic policy and joined in a buffet lunch.

She then returned to 10 Downing Street for the rest of the day. An aide said, "The prime minister is very upset and very distressed about her son, as any mother would be."

The car rally, which is also sponsored by Le Point magazine and the French radio station Europe No. 1, is one of several staged annually around the world. But it is the only one passing through such remote desert.

Previous participants said the track is marked by gasoline cans spaced every kilometer and it is easy to become disoriented and lost not far from the rally route in the sand or nearby mountains. But they added that the weather is mild this time of the year, and participating vehicles are well stocked with water, food, tools and repair parts. Three Italian journalists covering the rally died in the desert last year.

Verney, who had driven in the rally before, asked Thatcher to join her this year when they met at the Le Mans endurance race in France in December, according to Barry Gill, Mark Thatcher's friend and agent. Gill told reporters Thatcher was "very enthusiastic" and left for the rally after spending Christmas with his family at the prime minister's country residence at Chequers.

In a brief television interview in Paris before the rally began, Thatcher said he was not worried by his lack of experience in long-distance rallies. "Now that I've raced in Le Mans and other things," he said, "this rally is no problem."

Since being trained at Brands Hatch racing-driver school in England, Thatcher has been a moderately successful driver, surviving two serious crashes. His name has attracted considerable commercial sponsorship, particularly in Japan. He also has modeled clothes, promoted whiskey on Japanese television and worked as a management consultant.

His twin sister Carol, the Thatchers' only other child, was a television journalist in Australia for several years before returning to Britain in December. An aide to Mrs. Thatcher said the daughter is now living at Downing Street and looking for a job here.