The Reagan administration announced yesterday that it has granted political asylum to Hu Na, prompting expressions of appreciation and relief from the teen-age Chinese tennis champion and a threat of retaliatory action from the Chinese government.

The brief announcement by Justice Department spokesman Arthur Brill gave no details of the decision, reported to have been controversial within U.S. official ranks, that Hu, 19, had established "a well-founded fear of persecution" if she returns to China.

In a statement released through her attorney, Hu said, "If my family in China can hear my words, I hope they know that I still love them and miss them dearly. I hurt for my parents, brother, sister and grandfather, who have written to me.

"No one in China knew that I would take the action I felt I had to take last July" in deciding to defect from an international tennis tournament in California. "I hope they can understand my personal agony in making such a choice to leave my homeland," she added.

A letter written by a ranking Communist Party official in her home province of Sichuan reportedly played a role in establishing her claim in immigration proceedings that she was being pressured to join the Communist Party.

According to quotations cited by Associated Press, the official wrote shortly before she left for a U.S. tennis tour that she should "improve on your political outlook and commit yourself to a deeper socialistic attitude." The letter also said, according to the AP, that "the Communist Party is relying on you to be strong during these temptations in your life" and that she should report to the party to discuss joining it after her return from abroad.

The Chinese Embassy, informed of the decision after the public announcement, issued a statement protesting that "The U.S. government has no grounds whatsoever to take this course of action . . . . There simply does not exist any question of political persecution against her."

The statement called the grant of political asylum "a grave incident harming the relations between the two countries" and said it "will certainly affect bilateral exchanges."

The State Department had no comment on steps China might take regarding exchanges. About 10,000 Chinese citizens are studying here, but only 200 to 300 U.S. citizens are studying or doing research in China, officials said.

Immigration and Naturalization Service officials were widely reported to have hesitated about granting political asylum to Hu because of the potential impact on other cases.

INS said the latest data available shows that, as of last October, 1,030 applications for political asylum were on file from citizens of the People's Republic of China.

Only 27 Chinese applications for political asylum have been granted since a new immigration law three years ago eliminated a previous presumption that political refugees from all Communist countries were fleeing for valid reasons. During the same period, 187 requests for asylum from Chinese were denied, according to the INS.

Some elements of the State Department reportedly favored permitting Hu to remain here without formally granting political asylum, on grounds that this would be less of an affront to Peking. The final decision on the case is said to have been taken at high levels of the administration.

Hu, China's top-ranked woman tennis player in 1981, has been living with Chinese-American families in California while her case was pending.

She said recently that she would like to learn English and attend school before considering a future as a tennis professional.