BEIJING, China — The Vatican should take steps to improve relations with China, the Chinese head of religious affairs said on Tuesday, a week after the Roman Catholic Church said it was hoping for “positive signals” from Beijing.

Pope Francis is trying to heal a decades-old rift with China where Catholics are divided between those loyal to him and those who are members of a government-controlled official church.

One of the obstacles to improving relations is the question of who should be able to appoint senior clergy.

China says bishops must be named by the local Chinese Catholic community and refuses to accept the authority of the pope, whom it sees as the head of a foreign state that has no right to meddle in Beijing’s affairs.

Wang Zuoan, head of the State Administration for Religious Affairs, was quoted by state news agency Xinhua on Tuesday as saying China “hopes the Vatican takes an even more flexible and pragmatic attitude, and takes actual steps to create beneficial conditions for improving relations.”

China wants constructive talks to narrow differences, increase consensus and promote improved relations, he told a meeting of Chinese Catholics.

“The Chinese government’s position on improving Sino-Vatican ties has always been clear and consistent,” Wang said.

The Vatican said last week it was “certain that all Catholics in China are waiting with trepidation for positive signals that would help them have trust in dialogue between civil authorities and the Holy See and hope for a future of unity and harmony.”

The two sides have been at loggerheads since the expulsion of foreign missionaries from China after the Communists took power in 1949, and the Vatican’s continued maintenance of official ties with self-ruled Taiwan, claimed by Beijing as its own.

Prospects for a deal were set back this month after Lei Shiyin, a government-backed bishop excommunicated by the Vatican, participated in the ordination of new bishops.