Vatican Secretary of State Agostino Casaroli wound up a delicate mission to Czechoslovakia today that church sources said was part of a new papal push to restore the prestige and influence of the Roman Catholic Church in the communist-ruled nations of Eastern Europe.

Cardinal Casaroli refused to comment on his trip to commemorate the 1,100th anniversary of St. Methodius in the Moravian village of Velehrad. But Vatican sources were privately effusive about the turnout Sunday, when about 150,000 persons were reported to have cheered Casaroli and the absent pope and to have booed Czechoslovak government officials who also addressed the gathering.

Czechoslovakia has been particularly restrictive of the church. The significance of Casaroli's visit was underlined last week in a papal encyclical, "The Apostles of the Slavs," which hailed the historic role of the church in Eastern Europe.

The encyclical, the pope's fourth since assuming the papacy in 1978, was released to mark the anniversary of St. Methodius and his brother St. Cyril for their pioneering evangelical work among the Slavs.

That Prague had denied the pope an invitation he clearly sought to attend the ceremonies in Velehrad made the encyclical all the more pointed.

Although couched in the Vatican's usual cautious diplomatic wording, the encyclical elaborated on the Polish pope's previous insistence that the church offers a unique, historic bridge between the politically divided European nations of the East and West.

Using the example of the Greek monks Cyril and Methodius, the pope indicated that similar work by the church offered probably the only chance for reuniting Europe.

"By exercising their own charisma, Cyril and Methodius made a decisive contribution to the building of Europe," the encyclical stated, "not only in Christian religious communion but also to its civil and cultural union.

"Not even today does there exist any other way of overcoming tensions and repairing the divisions and antagonisms both in Europe and the world, which threaten to cause a frightful destruction of lives and values. Being Christians in our day means being builders of communion in church and in society."

The encyclical, according to Vatican sources, codified the decisive, if subtle, shift in the Vatican's policy toward Eastern Europe that has taken place since Pope John Paul II, a Pole who frequently confronted his own nation's communist leaders, was elevated.

Prior to that time, the Vatican's policy toward the East set by Paul VI and Casaroli was based on passive resistance.

That policy has shifted gradually under John Paul II, according to Vatican analysts, from simple accceptence of communist political power in the East to cautious challenge of that power from a moral, religious standpoint.

This emphasizes the current pope's contention that political systems, whether communist or capitalist, are ultimately more transient than the historical role of Christianity in world civilization.

"Unlike his immediate predecessors, who seemed impressed by communist political power in Eastern Europe, this pope believes it can be challenged and made to cede ground -- so long as the challenges are not political but moral, dealing more with demands for individual rights and religious freedom than political liberty," said a leading Rome analyst of the Vatican who asked not to be named.

"This pope is trying not just for detente with communism but actually to roll it back, but by attacking it on personal moral grounds rather than the sort of political grounds that can be interpreted as a challenge to the current temporal leaders of Eastern Europe's security consciousness."