By Patrick Oppmann, CNN

Havana (CNN) – Thirteen Cubans Thursday refused to leave a Havana church where they had spent the last three days in hopes of gaining a meeting with Pope Benedict.

The pope is due to travel to the island at the end of the month following a visit to Mexico.

The group described itself as "dissidents" and refused to leave Our Lady of Charity Church after arriving there Tuesday, according to a news release from the Havana Archdiocese.

The Partido Republicano de Cuba organization claimed the people occupying the church were members of the group.

In a phone interview with CNN en Español Thursday, the group's director said the organization wants political prisoners released, greater access to information and freedom to travel.

"We are not trying to tarnish the pope's visit. We are trying to get the church to serve as a mediator for dialogue between the Cuban government and the opposition," Vladimir Calderon said. "Really, we cannot find other routes, because the Cuban government, the regime, has not let us have access. ... That's why we haven't left the church. That's why we've done it like this, because there is no other way."

Church officials are trying to negotiate with the group, the archdiocese said, calling the action an attempt to embarrass the church before the pope's visit.

"No one has the right to turn temples into political trenches," the church release said. "It's clearly an illegitimate and irresponsible act."

In the release, Church spokesman Orlando Marquez said other groups around the country had carried similar protests on Tuesday but then had left those churches

So far, the church said it declined to ask the Cuban government to remove the group, the statement said.

The church's statement was also published Thursday in Granma, the official newspaper of the communist party in Cuba.

There was no visible police presence outside the church Thursday, and parishioners entered and left the building.

An elderly woman at the entrance to the church said the press was not allowed to enter.

In a statement Thursday, the chairwoman of the U.S. House Foreign Affairs Committee called on the pope to meet with critics of Cuba's government during his visit.

"It is my hope that Pope Benedict will show his support for the Cuban people by meeting with peaceful dissident groups, including those practicing their faith while bringing attention to human rights violations," Rep. Ileana Ros-Lehtinen said.

–CNN's Catherine E. Shoichet and CNN en Español's Lucia Navarro contributed to this report.