Even referring to the group as Rohingya, the cardinal warned, could weaken the democracy movement led by Ms. Suu Kyi and provoke a backlash by militant Buddhists against the country’s Christian minority.

Pope Francis has been outspoken about the group’s plight. In August, after the military began its crackdown in response to attacks by Rohingya militants on security outposts, the pope lamented what he called the persecution of “our brothers the Rohingya,” and called for them to receive their “full rights.”

Myanmar doesn’t recognize the Rohingya as citizens and refers to them as “Bengalis,” though many have lived in the country for generations.

Ms. Suu Kyi, Myanmar’s civilian leader, shares power with the military and has faced international criticism for her refusal to criticize the crackdown, in which the military has been accused of burning villages and killing and raping villagers. Myanmar authorities reject refugee accounts of such atrocities.

Next week’s visit, which ends Thursday, will be the first to the majority-Buddhist country by a pope, coming seven months after the Holy See and Myanmar established relations. The pope said in a video issued last week that he intends to bring a “message of reconciliation, forgiveness and peace.”

The visit is intended as well to “help a small church” in a poor, developing country, a Vatican spokesman said.

That applies as well to his subsequent stop, in majority-Muslim Bangladesh, where he will take part in a public inter-religious event at which he will meet a small group of Rohingya.

Hundreds of thousands of Rohingya refugees remain in camps in Bangladesh across the border from Myanmar. The neighboring countries said on Thursday they had agreed on the return of the Rohingya, but the process could take years.

The pope’s advocacy for the Rohingya has enhanced his image in the Muslim world and raised international pressure on the government of Myanmar, said Khairudin Aljunied, an expert on Islam in Southeast Asia at Georgetown University. “Muslims very much appreciate that the pope has spoken up for them,” he said.

Cardinal Bo lamented the military’s violent reprisals against civilians and the incitement of what he called “Islamophobia” by militant Buddhist monks. But he also said the outside world’s view of the crisis is shaped by “Muslim propaganda,” and expressed sympathy for the need for a military and public response to the threat posed by Rohingya militants.

The cardinal said he has counseled the pope to speak cautiously about the problem when in Myanmar, and has made a series of public warnings—extraordinary for a local church leader in advance of a papal visit—advising the pope on how to do that.

He said that together with the country’s bishops, he has urged the pope in particular to eschew the term “Rohingya,” which he said connotes claims to a historically unwarranted status as an indigenous ethnic group.

The pope’s use of the term could create an “uncontrollable” situation, such as large demonstrations, the cardinal said.

The pope is taking the cardinal’s advice very seriously, a Vatican spokesman said Wednesday, but “we’ll all have to see” what he chooses to do.

Cardinal Bo said the pope could refer instead to the Rohingya as “Muslims of Rakhine State”—the border state where the group was concentrated—and speak in general terms about ending ethnic conflicts in Myanmar.

The pope, at Cardinal Bo’s urging, added to his schedule a meeting on Thursday with Sr. Gen. Min Aung Hlaing, commander-in-chief of the Myanmar Armed Forces—an encounter that “might be a way that the pope could influence him and soften his heart,” the cardinal said.

Hard-line Buddhist leader Aye Maung warned that Pope Francis could provoke violence against Christians if he appears to express solidarity exclusively with Muslims in Rakhine.

“If the leader of the Christian community is biased, Buddhists will get very angry and upset. Violence will happen,” said Mr. Maung, chairman of the Arakan National Party, a political party that represents the interests of Buddhists in Rakhine, a community that sees the Rohingya as a threat to their livelihoods and safety.

There are about 650,000 Catholics in Myanmar and a total of 4.15 million Christians of all denominations, out of a population of 52 million. Protestants have said they fear that they, too, would be caught up in any backlash to the pope’s statements.

Rohingya activist Kyaw Min, chairman of the Democracy and Human Rights Party, a political party focused on representing Muslims, said it was disappointing that Catholic Church leaders were urging the pope to avoid using the word Rohingya.

If the pope doesn’t specifically address his community’s grievances, Mr. Min said it would “send the wrong message that the situation of the Rohingya is not that alarming.”