The killing of a popular Roman Catholic priest by secret police agents has brought not only a political crisis for the government but also new dilemmas for the Polish primate, Cardinal Jozef Glemp.

Before the slaying last month of the Rev. Jerzy Popieluszko, Glemp had trod delicately between dialogue with the Communist government and opposition to the state's atheistic ideology.

He had lent Polish leader Gen. Wojciech Jaruzelski conditional support in the interest of avoiding unrest and in the belief that Jaruzelski's rule is preferable to a more hard-line alternative. He had been moving quietly to constrain some of the more militant priests who had drawn government objections.

At the same time, the Roman Catholic Church had become shelter for an array of political activities during Glemp's 3 1/2 years in office.

Popieluszko's brutal killing has complicated the primate's balancing act. On the government front, all talks on matters of joint church-state concern are now frozen, according to a senior legal adviser to Glemp. On the church front, the primate confronts an embittered clergy whose ranks are likely to produce more priests aspiring to take Popieluszko's place as patron of the Solidarity movement.

An early test case for Glemp will be what he does about the scene at St. Stanislaw Kostka Church in Warsaw, where Popieluszko served and is buried. Solidarity sympathizers have turned the church into a kind of opposition sanctuary, hanging Solidarity banners on the railings, holding press conferences in the churchyard and distributing information critical of the government. Naturally, the authorities find so blatant a display highly objectionable. Church officials have made some attempts to remove lay activists and opposition emblems.

It is generally expected here that in time, political pragmatism will pull Glemp and Jaruzelski back to the negotiating table. Now more than ever the general needs the cardinal's tacit assistance against his hard-line rivals to show that church-state rapprochement is Poland's only way toward peace.

The church, in turn, is anxious to conclude talks on projects sure to enhance its own standing, including a church-sponsored fund to channel western assistance to private farmers and a law recognizing for the first time the church's legal status in Communist Poland.

But facing both sides is the nagging question of just what role the church should play in political life. The answer to this can trigger violent disagreement in the party's own ranks. Capt. Grzegorz Piotrowski, the leader of the three-man team charged with the killing of Popieluszko, is claiming that he acted out of frustration with what he felt were Jaruzelski's ineffective attempts to curb antistate church activity.

The outlawing of Solidarity and the muzzling of once outspoken cultural associations has left the church the only institution in Poland independent of Communist control.

To co-opt the church into the political process, Polish authorities have conceded at least a limited political role to the Catholic leadership. Church officials are invited to comment regularly on legislation. Earlier this year the church mediated in negotiations to free the imprisoned leaders of Solidarity and the dissident Committee for Social Self-Defense (known by its original Polish initials KOR).

The government has welcomed church pronouncements on political themes when the church view has coincided with the official line -- in calling, for instance, for the lifting of U.S. economic sanctions against Poland or in chiding West German Catholics for raising the issue of a German minority in Poland.

It would have also welcomed a statement by the church urging Poles to vote in last June's controversial local elections. But the episcopate remained silent on the matter, which was itself a political act. Authorities visibly squirmed in the months before last summer's amnesty when the church pressed demands for the freeing of all political prisoners.

Where the main dispute arises is over the church's association with opposition activity. Dozens of priests around the country use their pulpits to preach an attitude of wariness toward the government. Popieluszko was the best known of this group, along with the Rev. Henryk Jankowski of Gdansk, the pastor of Solidarity leader Lech Walesa.

Pulpits are often occupied, too, by lay activists delivering antistate messages. Under church roofs, seminars meet on subjects considered taboo by the authorities. Solidarity emblems appear on religious pilgrimages and inside church buildings. Uncensored plays are staged in churches, and underground art is sometimes on display there.

Defending their involvement in such things, Polish clergymen contend that the church must encompass many aspects of life. Moreover, the Polish church, as guardian through the centuries of Poland's national identity, claims a social as well as religious mission. By his own example, too, Pope John Paul II, Poland's most famous Catholic, has asserted the church's duty to speak out for freedom, truth and human rights.

The protection the church provides antistate activities and the politics priests are playing were coming to a head as an issue in party discussions at the time Popieluszko was slain. A report last month on topics for debate by the Communist Party Central Committee cited "persistent hostile" actions in Catholic churches.

It complained of a "tendency among political clerics to lead the church past its wide framework of religious activities," a tendency, the report said, that could "damage the basic foundation of the separation of church and state." It warned that "the state cannot be and will not be indifferent to such a phenomenon."

In the shock of the Oct. 19 killing of Popieluszko, a major showdown in the party on the church question was avoided. Judging by published excerpts of speeches, the Central Committee meeting held a week after the priest's death heard only muted criticism of Jaruzelski's tolerant policy toward the church.

But the party's growing irritation with outspoken clerics was stressed again in a communique this week by the ruling Politburo. Communist leaders complained of clergymen among those using gatherings in religious shrines "to revive openly antistate activities."

Opposition members have said the Jaruzelski government bears moral responsibility for the Popieluszko killing by inciting hatred against the pro-Solidarity cleric and other militant priests.

In fierce rebuttal, government spokesman Jerzy Urban and Zdzislaw Morawski, editor of the main Warsaw daily Zycie Warszawy, countered this week that some Solidarity activists and priests were the ones conducting a hate campaign -- in this case, against the regime.

Signaling an internal church review of its place in Polish politics, Glemp's council of lay advisers has begun a study on "the church and politics."

In the meantime, Glemp hesitates to address the issue publicly. At Popieluszko's funeral, he noted that the priest's life raised the question of political sermons but then ducked the subject, saying a burial was no place to discuss it.

He did offer one line that appeared to defend activist priests. "The love of homeland as a form of loving your brothers," said the cardinal, "cannot be only an abstraction but finds forms of social engagement."