He said the delegation was traveling on behalf of the Diocese of Rome, which is promoting the late cardinal's sainthood cause.
Delegation members had asked for tourist visas and had not gone through the Vatican's diplomatic channels, Father Benedettini said.
The Vietnamese Embassy in Italy withdrew the visas, reported AsiaNews, a Rome-based missionary news agency.
Cardinal Turkson, as head of the justice and peace council, is helping with the process of beatification of Cardinal Nguyen Van Thuan, who served as president of the same council from 1998 to 2002.
The Vietnamese cardinal died in Rome in 2002 at the age of 74.
Vietnam's communist regime jailed Cardinal Nguyen Van Thuan in 1975 when he was the newly named coadjutor bishop of Saigon, later renamed Ho Chi Minh City. He was never tried or sentenced and spent nine of his 13 years of detention in solitary confinement. His uncle was South Vietnamese President Ngo Dinh Diem, a Catholic who was assassinated in 1963.
The church and religious activity face strict controls in Vietnam, though some parts of the country have seen a gradual easing of restrictions on Catholic practices.
In 2010, Vietnam agreed to let Pope Benedict XVI name a papal representative to Catholics in the country and, several months later, accepted the pope's appointee as a first step toward diplomatic relations.