Archbishop Joseph Glemp, the Roman Catholic primate of Poland, flew to Rome today amid signs that the country's martial-law authorities oppose plans for a papal visit next month.

Glemp is making what church officials called a regularly scheduled visit to the Vatican. But speaking to reporters at Warsaw's airport, he said he would "report to the pope on the wishes of the nation" regarding the pontiff's visit, originally scheduled to coincide with ceremonies Aug. 26 marking the 600th anniversary of the country's most sacred shrine, to the black madonna at Czestochowa.

Asked if Pope John Paul II could be expected next month, Glemp replied, "Why link his arrival to August?"

Upon reaching Rome, Glemp said he could make no statement on the "precise date"of the pope's visit, United Press International reported. "I can only express my hope that it will be possible to receive him in a dignified way in Poland in the near future," he said. Glemp and the pope met privately, and the Vatican released no details of their talks.

According to a Polish church official, the government has expressed deep misgivings over the timing of the visit and has suggested that the pope come later in the year. He said apprehension stemmed from concern that public "emotions are running high" at the moment and that no security force would be large enough to absolutely control the millions of Poles assembled, some of whom might try to "get even" with the police. Numerous clashes have been reported between Poles and police since the government crackdown Dec. 13.

An August visit would come at a politically sensitive time. Aug. 31 is the second anniversary of Solidarity's formation, and many Communist officials are said to believe that a papal visit so close to that date could stir the wrong kind of emotions.

Some authorities reportedly prefer that the pope's visit not come until "normalization" has been achieved, so that he could be seen as giving his blessing to it. They contend that John Paul's presence in Poland during a period of calm would further stabilize the country and strengthen the role the Catholic Church has played as a bridge between authorities and a disenchanted citizenry.

In the view of many of these authorities, August is too soon for such a visit to have this effect.

Diplomatic and church sources here are predicting that many of the nearly 3,000 political prisoners now in their seventh month of detention will be released on or before Poland's national day, July 22. Some martial-law restrictions may also be lifted, according to the same sources.

To carry out these changes, the authorities may want a period free of the powerful presence of the pontiff, who is a popular rallying point in this overwhelmingly Catholic country and who some in the government fear will kindle strong anticommunist sentiments.

The pope has been a critic of martial law since its imposition Dec. 13 and has called for the release of political prisoners.

The last trip of John Paul in July 1979 is widely credited with serving as a catalyst for the rise of Solidarity the next year, because it gave Poles a renewed sense of unity.

Earlier this year, Vatican officials reportedly felt that the pope should not be put in the position of appearing to endorse martial law by his presence in Poland.

But the pope's recent trips to Britain and Argentina at the height of the Falkland Islands fighting was thought to have set a pattern for a purely pastoral visit to his homeland that would sidestep conditions for a visit such as the lifting of martial law or the release of political opponents imprisoned by martial law authorities.