By David Adams HAVANA (Reuters) - This week's three-day visit to Cuba by Pope Benedict marked another milestone in the Roman Catholic Church's cautious efforts to expand its role in the communist-run island. Havana's Cardinal Jaime Ortega called it a "Springtime of faith." While it remains unclear if or how the visit will change anything in Cuba, most analysts agree any notion of a "Cuban spring' in terms of political change is still a long way off. Even so, the visit seems to have ensured a growing role for the Church in Cuban society and politics, a potentially significant shift in the balance of forces in a country where religious faith was once scorned. The Catholic Church in Cuba has taken on a larger role. For the first time it is in a direct dialogue with the government, direct dialogue having to do with domestic policies," said Philip Peters, a Cuba expert and vice president at the Lexington Institute, a Virginia-based think tank who attended Wednesday's Havana Mass. The Church is pushing more and deeper economic reforms. The Church is also pushing for political openings. The Church hopes primarily that the papal visit will help spark a spiritual revival in Cuba, where religious faith was stigmatized for decades after the 1959 revolution. Despite that, a much diminished Church survived and remains the largest and most socially influential institution outside of the government, a fact that Cuban leaders now seem more willing than ever to recognize - and perhaps reward. Pope Benedict used the trip to deliver a shopping list of requests in talks with Raul Castro on Tuesday, including official recognition of Good Friday - barely a week away - as a national holiday, as well as pressing for greater access to the media and the right to open religious schools. In fact, the Church has in recent years taken some baby steps in the field of education by offering after-school programs at a handful of churches, as well as university classes offered by a Spanish Catholic order, the Escalapios. Late last year the government even allowed the Church to open a part-time Master's in Business Administration program at a Havana seminary with the help of Catholic University professors from Spain. Benedict's visit came 14 years after Pope John Paul's groundbreaking trip in 1998, which many Cubans say was the beginning of the thaw in church-state relations. While Fidel Castro received the pope warmly in 1998, his brother and current president, Raul Castro, was even more attentive on this latest papal visit, attending the two Masses celebrated by Benedict, seated in the front row. Critics, especially the hard-line Cuban-American exiles in Miami, as well as some human rights activists in Cuba, consider the transformation in church-state relations an unholy marriage of convenience, opening the Church up to accusations of not doing enough to defend the human rights of the island's political dissidents, who the Cuban government considers as mercenaries of the United States. The Church argues that its engagement with the government is a necessary acceptance of Cuba's political reality. The church is not going to dismiss a political system outright. The church will always work within the constraints of a system to find ways to improve human life and dignity," said Father Juan Molina, director for Latin America affairs at the US Conference of Catholic Bishops. Nor has the Church given up on a democratic opening. "While improved relations are in the interest of both the Catholic Church and the Cuban government, it is also clear that the Church would like to see political reform on the island," said Geoff Thale, program director for the Washington Office on Latin America, a liberal think tank in the U.S. capital. "While we may not see immediate actions on human rights in Cuba," as a result of the pope's visit, Thale said it had "strengthened the Catholic Church's ability to open space for dialogue and debate ... essential to building a climate that favors human rights." In his public addresses in Cuba, the pope made repeated references to the need for "authentic freedoms" essential to the building of a "renewed and open society." Raul Castro seemed to have no problem with that, noting in his final remarks before the pope departed that there were many areas where the Cuban government coincided with the views expressed by the pope, "though it's natural that we don't think the same way on every issue." For Cuba, the pope's visit offers much-need legitimacy in its quest for international acceptance, all the more so given the health of their main political and commercial ally, Hugo Chavez, president of oil-rich Venezuela, who is battling cancer and faces a tough re-election in October. One key area where the Church and the Cuban government share common ground is over the island's need for economic changes to raise living standards. Since taking over the reins from his ailing brother nearly six years ago, Raul Castro has introduced tentative but ever-more-ambitious economic reforms to overhaul Cuba's rickety Soviet-style economy, including slashing a million government jobs and freeing up some business sectors to small-scale private enterprise. Recognizing that these reforms are a difficult adjustment for Cuba after decades of tight economic and social control, Benedict used his visit to offer the Church's "constructive" support "in a spirit of dialogue to avoid traumas." The pope's message of renewal and reconciliation resonates with Cubans looking for change. The country needs economic reforms and physical reconstruction, but there's also a huge job of moral reconstruction. Christianity can help us," said Oscar Espinosa Chepe, a moderate voice within the island's dissident movement jailed for "crimes against the state" in 2003 before being freed in 18 months on medical grounds. Some Cubans remain skeptical about the Church's role. The Church does not need greater weight in society. I think society as it is works well. We have healthcare and education," said retired teacher Esperanza Gonzalez, 66, who attended the pope's Havana Mass. "We are ready for reconciliation, but I don't think the exiles in Miami want that," she added. But the pope's message is earning currency among Cuban-American exiles who, while wishing for a faster pace of change, also recognize the pitfalls. "You don't change from a totalitarian society to an open society without a lot of pain, without a lot of sacrifices," said Carlos Saladrigas, a Cuban-American businessman from Miami who also traveled to Cuba to attend the pope's masses. What the church is advising us is that we need to do what we can to facilitate making change easier for all Cubans. In the words of the Archbishop of Miami, Thomas Wenski, who led a group of several hundred Cuban-American on a special papal pilgrimage to Cuba this week: "The interests of the Holy Father and the church here in Cuba is that whatever transition comes, that it be a soft landing." Additional reporting by Simon Gardner in Havana and Kevin Gray in Miami; Editing by Philip Barbara