Iran said Tuesday it had formally protested the F.B.I.’s arrest of an American newscaster who works for the Iranian government’s Press TV, and her family said rallies in Washington and elsewhere were planned if she was not freed.

The arrested American, Marzieh Hashemi, has been held for more than a week as a material witness in an unspecified criminal case and has appeared before a grand jury in Washington twice. She has not been charged with a crime.

Iranian officials have seized on the arrest as a provocative new irritant in the tense relationship between Iran and the United States, which has worsened since the Trump administration renounced the Iranian nuclear agreement last May and reimposed severe sanctions on the country.

Ms. Hashemi, 59, who has lived in Iran for more than a decade and travels back to the United States sometimes to visit family members, was arrested Jan. 13 in St. Louis and transferred by the F.B.I. to Washington.