A group of Cuban exiles who are cautiously lobbying for normalized relations with the government of Fidel Castro have suggested that the U.S. government poll "rank-and-file Cubans" living here to determine their views on the issue.

Three members of the Cuban Group for Family Reunification came to Washington to press at the State Department and on Capitol Hill for an end to the embargo on trade with Cuba.

In a statement handed to legislators, the group said: "Everybody in this country believes that Cubans living in the United States oppose restoration of diplomatic relations between the U.S.A. and Cuba. That is a myth. We can assure you that a great majority of Cubans living in this country wants U.S. to lift the economic embargo of Cuba and to normalize relations."

The group said a "small minority" opposing ties with Cuba "controls the Spanish news media in the U.S.A., backed by powerful economic and political groups." The statement added that "extremist groups" used terrorist tactics in the Cuban community "to silence public opinion."

The three middle-aged men who came to Washington to present the group's views asked that their last names not be published.

"In Miami they kill people," said Fernando, who has been separated from his wife and two daughters since he left Cuba in 1968. He was refering to a number of bombings and political assassinations involving Cuban exiles in recent years.

Another member of the group, Miguel, said it had recruited its approximately 100 members through ads asking exiles separated from their families to write to a post office box.

"We are very careful," he said.

Miguel said most members of his group do not support the Castro government, but hope that normal trade and diplomatic relations will be established so they can be reunited with their families.

The source said some Castro opponents had suggested that the group might be used by the Cuban government to pressure Washington, but added that despite that possibility many people were sincerely interested in seeing their families again.

Miguel estimated that as many as 1,000 Cubans in the United States are separated from close relatives - spouses or children - who have not been allowed to leave the island.

The group gathered letters from many of the exiles and Sen. James Abourezk (D-S.D.) handed the letters to Cuban officials when he visited the island in December. There has been no response.

All three said they would not [WORD ILLEGIBLE] to return to Cuba, but hoped to bring their families here.