Andrei Sakharov, the dissident Soviet physicist and Nobel Prize winner, reported today that he and his wife "are okay" on the 10th day of their hunger strike.

"We are holding on cheerfully, we are following our regime," the 60-year-old Sakharov said in a telegram.

The cable sent from the industrial city of Gorki, where Sakharov was banished almost two years ago, was the first direct communication from him in five days. The physicist started the protest Nov. 22 to press the government to allow his stepson's wife to emigrate to the United States.

In two separate statements made available here, Sakharov denied reports that his condition has worsened and said this was based on disinformation spread by the KGB security police. He also vowed to continue his protest against the "irresponsible, cruel and illegal" act of the state's holding the young woman, Lisa Alexeyeva, "hostage."

"Now the only possibility of terminating our hunger strike is Lisa's exit "from the Soviet Union," he said. He also said that he has not been receiving telegrams from Alexeyeva, which she said she has been sending to Gorki each day.

"We are holding on, our mood is one of determination, and we are feeling so far quite fine, all the symptoms and indications correspond to those in the books," he said. His wife, Yelena Bonner, is a physician.

The physicist had said earlier that he would stage a hunger strike because he had exhausted all other ways to persuade authorities to let Alexeyeva join Bonner's son, Alexei Semenov, who is a graduate student at Brandeis University. Sakharov said the government was denying exit to Alexeyeva as a form of revenge and pressure on him to curb his dissident activities.

Sakharov is one of the most famous Soviet scientists. He was elected to the Soviet Academy of Sciences at age 32 for work in thermonuclear physics, which led to the development of the Soviet hydrogen bomb.

The legal aspects of the case for which he has gone on hunger strike are somewhat murky. Semenov has been married previously and his wife and child had emigrated to the United States 18 months ago. They have since been divorced. He married Alexeyeva in a proxy ceremony in Montana last summer.

There has been considerable concern here in intellectual circles about the state of Sakharov's health. He is said to be suffering from a common form of heart disease in which the supply of freshly oxygenated blood to the heart is restricted. Bonner is also in poor condition, having become a partial invalid from wounds suffered in World War II.

Well-informed sources said the physicist stopped taking medicine for his heart condition when he began the strike because fasting may cause the drugs to have an adverse effect. The Sakharovs are taking only mineral water.

In an earlier statement, Sakharov expressed his thanks for American statements of support and voiced the hope for "analogous help" from European governments and European scientists.

In a reply to an appeal from the Federation of American Scientists to discontinue the hunger strike "while your supporters help you achieve your goal," the physicist said that "I cannot anymore believe any promises made by the authorities that are not supported by actions."

He said he would continue his protest if Alexeyeva is not permitted to leave the Soviet Union. "I ask you please to understand this correctly," he said.