Apparently inspired by a recent hunger strike by Andrei Sakharov and his wife, two Soviet women who have lived in the U.S. Embassy compound here for 3 1/2 years in hopes of emigrating to the United States have started a similar strike to press their demands.

Augustina Vashchenko and her daughter Lydia, who started the protest on Dec. 28, are two of seven Pentecostalists who ran past Soviet police guards into the U.S. Embassy on June 27, 1978, saying they were being subjected to religious persecution in the Soviet Union.

The seven have been living ever since in a 20-by-12-foot basement room. They are Pyotr and Augustina Vashchenko and their three adult daughters and a mother and son, Mariya and Timofey Chymkalov. All have been holding out for guaranteed emigration for their entire families.

The Vashchenkos have 13 children, most of whom remain in their native mining town of Chernogorsk, where Mariya Chymkalov's husband also lives. The number of relatives involved is 22.

Mrs. Vashchenko and her daughter said they would continue to take only tea and fruit juices until their problem is finally "resolved." They have told American officials that they would refuse to be hospitalized in a Soviet institution.

Officials quoted an embassy physician as confirming that the fast has begun to show its effects on the two women. Their situation was not described as serious, however.

The Soviets so far have refused to provide advance assurances that the two families would be allowed to leave.

Although the Americans here could hardly turn these refugees out into the street, they have been hoping that the seven would leave voluntarily.

The hunger strike could bring the issue to a head. The two Vashchenkos said that President Reagan had appealed personally to Soviet President Leonid Brezhnev recently to yield to emigration demands that led nuclear physicist Sakharov and his wife to stage a 17-day hunger strike. Reagan "should do the same for us," Lydia Vashchenko said.

She continued: "We have been trying to leave the country for 21 years, and the Americans have not helped us at all. The hunger strike is like a kick in the pants for the Americans who think that what we are doing is stupid and that we are fanatics."

Augustina Vashchenko said: "The Americans say that the Russians must decide the issue, but we do not really know who or what is holding us here."

Soviet authorities have insisted that the refugees return to their native town and apply for emigration.

The husband of Chymkalov reportedly traveled to Moscow yesterday and showed up in front of the embassy accompanied by unknown men who offered to escort Mrs. Chymkalov to the Soviet passport office and pledged that she would be able to return to her embassy refuge.

Mrs. Chymkalov is said to have agreed to accompany the men but apparently changed her mind as she was about to leave U.S. territory.

Warren Zimmerman, deputy chief of mission, conferred this morning with the two protesters in an effort to persuade them to abandoned their hunger strike. Apparently he was not successful, since senior officials said later that they were saddened by the whole incident.

The embassy here does not have adequate medical facilities to treat the two women should their condition worsen. The mission will then have to decide whether to take them to a Soviet hospital despite their declaration that they would refuse such action.

"We would rather have the Americans send us back to the Soviets than continue living in that small room," said Lydia Vashchenko. "We will not leave the embassy grounds ourselves because that would be like committing suicide."