HANOI — Two musicians in Vietnam whose topical songs are popular among overseas Vietnamese were sentenced to prison Tuesday, prompting criticism from the United States and international rights groups.

Vo Minh Tri and Tran Vu Anh Binh were sentenced to four and six years in prison, respectively, on charges of spreading propaganda against the state, said Tri’s lawyer, Tran Vu Hai. They faced possible sentences of up to 20 years.