For the first time in Poland under communism, regular Sunday Roman Catholic mass was broadcast on the radio this morning in keeping with a government promise in an agreement with striking workers last month.

Bishop Jerzy Modzelewski, the Warsaw auxiliary prelate who conducted the service, dedicated it to the mass media.

"We thank God that our desires and prayers were listened to," he said before a crowded attendance at Warsaw's Holy Cross Church. "Every Catholic society has a right to use the mass media." His words were beamed on five wavelengths across Poland.

Leading the congregations in a round of petitions, the bishop said, "Let us pray that radio, film and television could serve the glory of the Lord and the progress of mankind . . . Let us pray for the employes of radio, press and television that they contribute to the moral development of mankind . . . Let us pray so that we could use radio, film and television in line with Christian principles."

Today's 9 a.m. broadcast was the first of what the government has pledged will be a regular Sunday event. Until now, Poland authorities had refused to allow religious programming, resisting repeated pleas by the church that broadcasts of church services were necessary to reach Roman Catholics who were sick, disabled or working.

Exceptions were made recently in allowing transmission of the installation in Vatican City of Polish-born Pope John Paul II. Some of the masses said by the pope during his visit here in 1979 were also telecast.

But in keeping with the hostile line generally taken toward religion by communist states, the Warsaw government had blocked regular church access to the media. Reversal of this policy was one of the 21 demands pressd by striking Baltic shipyard workers.

Poland's indentification with the Catholic Church dates back to the baptism of its first ruler, Prince Mieszko I in 966. Today, about three-fourths of Poland's 35 million people are practicing Chatholics, despite the state's official atheistic ideology. As an enduring stronghold through almost two centuries of foreign domination, the Roman Catholic Church remains a symbol of Polish natinalism and anticommunism.

Such widespread home support has made Poland's Catholic Church the largest, most influential and best organized religious institution in Eastern Europe.

However, the church exercises its authority cautiously. It plays the role of a sort of loyal opposition, pressing demands while cooperating with the government in times of crisis and knowing when to moderate its criticism of official policy.

In today's broadcast, for instance, Bishop Modzelewski paraphrased instead of reading directly a sharply worded letter release yesterday by the church attacking state-run television for disseminating "dishonest propaganda" and false moral principles. The letter was read in full at other masses in churches throughout Poland.

The bishop also made no mention of Poland's current and economic and political crisis.

During the recent period of major strike activity, the church took an evenhanded position, expressing support for workers' goals but implicitly criticizing their methods. Senior church officials appeared to remain aloof from the struggle.

Behind the scenes, though, they were promising in talks with government authorities to do everything to maintain social peace, as long as the government did justice to working class demands and resolved the conflict peacefully.

A serious church-state row developed midway through the critical strike at the Gdansk shipyard. On Aug. 24, the government took the extraordinary step of televising the message delivered by Cardinal Stefan Wyszynski in which the senior Polish cleric warned against prolonged protest and urged the strikers to get back to work.

The message, it turned out, had been edited by government authorities, with the cardinal's words of sympathy for the strikers deleted from the original text. Poland's primate was "furious," according to an aide. The church lodged a formal protest, but the damage had been done.

In any case, strikers ignored the cardinal's back-to-work plea and stood firmly by their demands. Some government officials like to point to this episode as a sign that the authority of the church in Poland has weakened along with their own.

Church officials do not feel they were snubbed, however.

"The main thrust of the cardinal's sermon was self-determination," said and aide to the primate. "He was not directing them back to work."

After the Baltic Coast strike ended -- with workers winning the right to form independent trade unions -- the church moved quickly to lead formal support to the new movement. The cardinal invited Lech Walesa, the Gdansk strike leader, to a private mass, and the two men later reportedly discussed how to organize new unions.

Church officials see their supporting role for the new labor movement as natural under Poland's current conditions.

"I think the new union leaders realize they cannot get in touch with dissident political groups for help," said the cardinal's aide. "So they see the church as something which they can go to because it is neutral."

Poland's church is neutral in the sense that it does not have a publicized political program. But there is little question how it feels about the communist government here.

From time to time Poland's bishops speak out forcefully on official policy.

Last December, they voiced "deep concern" about Warsaw's apparent inability to deal with Poland's econimic problems. They also attacked the practice of picking managers and government administrators on the basis of party loyalty over merit. They said existing policy had created "a serious moral crisis in Polish life."

In February and again in May, the bishops called on the government to end intensified reprisals against dissidents, declaring that no one should be victimized for holding views contrary to those of the regime.

While aligning itself with the advocates of reform, however, the church tends to stop short of calling outright for political change. Rather, the clerics prefer to show they are aware of the country's problems and present themselves as custodians of Poland's moral order.

Several times in the last three years, for instance, civil rights activists have urged church premises to stage hunger strikes. Church officials, distancing themselves from the actions, objected to the use of church property for political ends. At the same time, they voiced support for those fighting for human rights.

Church officials also worry about taking actions that might jeopardize their own sensitive negotiations with the state over issues vital for future church work.

The church's list of demands is long. It includes more access to the public media, permits for church construction, less censorship and more publishing of religious books and newspapers, discontinuation of mandatory Sunday work shifts, permission for independent church organizations, an end to discrimination against practicing Catholics, wider possibilities for religious education and official recognition of the legal status of the church in Poland as a public institution.

The last two are considered especially important. The church has made a considerable effort to reach young people and wants to give religious instruction in schools. Currently, chuch teachers often must give instruction in homes.

The triumphal visit of the pope to Poland, which showed the continuing attachment of the masses to the church, was thought to have strengthened the church's hand. But church authorities say their relations with the state have not changed much since.

There have been some concessions in recent months, including exemptions from the draft for seminary students and insurance and pensions for an increased number of clergy. The more significant result of the pope's visit, though, can be seen in numbers for church attendance and new seminary students. Both figures have shot up.

Under the new labor agreement, the government is committed not only to regular Sunday mass broadcasts but to giving religious groups greater access generally to the media. There are 29 denominations in Poland in addition to Roman Catholic.

"I interpret that point in a broad way," said Aleksander Merker, deputy minister for religious affairs, "meaning not only enlarging the Catholic press, but also providing more information about church life in Poland in the general press."

He noted that a visit to Poland earlier this month by a group of senior West German bishops was given feature play on Polish television. "This is something new in comparison with the old practice," Merker said.

At the same time, he said that, because of paper shortages made worse by the strike, there would be difficulties in enlarging the circulation of the Catholic press. The Catholic monthly Wiez, for instance, is limited to 7,000 copies, and the major Catholic paper Tygodnik Powszechny is kept to 40,000 copies.

Despite their difficulties, the church and Polish government have managed to establish a working relationship. The state seems to recognize it needs at least tacit church cooperations to ensure public support for its policies, especially in times of crisis.

Church-state contacts occasionally take place at the highest level. Cardinal Wyszynski, who is 79 years old and has been primate for 32 years, used to meet several times a year with ex-party chief Edward Gierek.

Stanislaw Kania, the new party leader, is known well to some senior church officials because he once had charge of church-state relations for the party. He is regarded as tough but fair.

With the birth of the new independent trade union movement -- and its success so far in winning media access for the church -- the question arises whether the church will use the new unions to pursue more of its demands.

"The new movement won't make much difference to us in that sense," said the cardinal's aide. "We had and have the proper channels for dealing with the government. The new trade unions must pursue their own goals."

But this official saw the new unions as helping in another way to fulfill one of the church's key aims: making Poles more aware and socially active.

"The result of the past system was to foster indifference. Now, by these unions, a great many people are being mobilized, and this is a very great success," said the aide.