A boatload of anti-whaling activists sailed yesterday into Nome, Alaska, claiming that seven others in their group had been arrested Monday by Soviet soldiers after sneaking into Siberia to spy on a Soviet whale-processing plant.

Bleary-eyed and exhausted, the 16 men and women told a startling tale of environmental espionage, complete with film footage and photographs.

They said that they crossed the narrow Bering Strait in the 147-foot trawler Rainbow Warrior, penetrated Soviet waters and distributed anti-whaling leaflets in the Siberian village of Lorino.

Then, they said, they encountered a truckload of armed Soviet soldiers who seized their friends. They said that they sailed about 200 miles back to Alaska under hot pursuit by Soviet vessels and helicopters for more than an hour.

The Soviets "were obviously very flustered," said Bob Cummings of Vancouver, British Columbia, who said that he saw the arrests through binoculars from the trawler about one-fourth of a mile from shore.

He said that Soviet soldiers yelled orders in Russian for the group to remain, and helicopters dropped cartridges containing pieces of paper with the message in English: "Stop Immediately."

"That's when we decided it was time to leave," Cummings said.

Cummings and the rest of the crew belong to Greenpeace, an international environmental group known for its media-grabbing protests against whaling, nuclear-waste dumping and atomic testing. They said that their mission was to draw attention to the Soviet killing of whales as the International Whaling Commission convened in England.

The incident set off a round of international diplomatic activity. Canadian and American officials asked the Soviet foreign ministry in Moscow for information on the six Americans and one Canadian and for access to them. There was no official Soviet response by late yesterday, and the State Department said that it could not officially confirm the incident.

"Something obviously happened," a State Department official said. "But one wants to check carefully since this is a group that has shown a certain disregard for what we call the common modalities."

Members of Greenpeace, a pacifist and environmental group, have protested Soviet whaling on the high seas since 1975. They have chained themselves to Spanish vessels to protest dumping of nuclear waste in the ocean, and one group claimed to have escaped under cover of night after being detained by the Spanish Navy in 1980.

In the latest incident, a group of 23 sailed from Vancouver on June 12 to protest whaling by the Soviet Union and Japan. Six of them, including U.S. Greenpeace director Chris Cook of Washington, went ashore at Lorino early Monday and radioed to the rest of the crew that they had photographed what appeared to be a modern whale-processing plant.

The six handed out Russian-language leaflets to workers in the plant, asking their support for Greenpeace's campaign against whaling.

Then, according to Greenpeace member Rick Dawson, a truckload of armed Soviet soldiers drove up, ordered the six to stand in a circle and took them into custody. Soon afterward the 17 other protesters began steaming back toward Alaska, Dawson said.

Jim Henry, of Orrs Island, Maine, was dispatched in a motorboat with color film footage and black-and-white still film to make a run for Nome on his own.

But according to several accounts, a Soviet helicopter dipped down and plucked Henry out of the boat, and the group last saw him dangling in the fog from the aircraft.

Cummings said that Bruce Abraham of Seattle then jumped from the Rainbow Warrior to the motorboat and managed to retrieve the film, breaking his leg in the process.

A commercial freighter and a Soviet warship appeared minutes later and began chasing the Rainbow Warrior, launching two speedboats and two helicopters, according to the Greenpeace skipper, Peter Willcox of Norwalk, Conn.

The Greenpeace ship zigzagged through the Bering Strait in an effort to escape as the Soviets radioed orders to halt, Willcox said. The Soviets then radioed the Warrior to ask its destination, according to several crew members.

"Nome unless fired upon," came the answer, according to radio operator Dick Dillman, a Greenpeace member who monitored the radio messages from San Francisco.

"Getting quite hairy. They're playing chicken with us," the Warrior radioed Dillman soon afterward as the Soviet ships gave chase. "Last pass was less than 20 feet away . . . . Peter Willcox advised them we won't stop, and gave them the finger."

The crew said that the warship chased the Warrior into international waters, beyond the 12-mile radius marking Soviet territory, but turned away about an hour later.

Abraham delivered some of the film to reporters when he arrived in Nome and was hospitalized for treatment of his broken leg. A French crew member flew to Seattle with color film footage of the arrests in Lorino and the escape at sea.

The mission apparently succeeded in drawing attention to the Greenpeace cause. Reporters from several countries crowded into Nome yesterday, and a Greenpeace dinghy ferried them and their camera crews out to the Warrior, where the crew granted interviews. One network reportedly paid the Frenchman's air fare from Nome to Anchorage.

Besides Cook and Henry, the other five left behind were identified as Pat Herron, 32, of Seattle; Nancy Foote, 35, of San Francisco; Barbara Higgins, 25, of Philadelphia; Ron Precious, 35, of Vancouver, and Dave Reinheart, 30, of Albany, Ore.

Cook, 35, had joked to a friend earlier this month about the possibility of getting arrested in the Soviet Union.

A friend here described him as having a longtime interest in "conservation, saving the environment and making the world better all around."

His mother, Betty Cook of Mayfield, Ky., said in a telephone interview that her son became interested in environmental issues partly as a result of "his upbringing and his sensitivity that led him to appreciate helpless creatures . . . . I save trees, he saves whales."