HAVANA (Reuters) - Cuba's Roman Catholic church leadership in a letter to parishioners called on the communist-run country's leaders to "update" the political system to allow more freedom similar to liberalization undertaken in the economy.

The statement by the Cuban Bishops Conference, presented to the press on September 16 and read in churches the day before, praised "incipient" reforms such as allowing small private businesses, more freedom to travel and buy personal property and the release of political prisoners, while at the same time urging a broader economic and political opening.

"We believe an updating of national legislation of a political nature is indispensable, as has been occurring in the economic realm," the bishops said in their letter.

"Cuba is called upon to be a plural society ... There must be a right to diversity in terms of thought, creativity and the search for truth," the statement added, without explicitly demanding a multi-party system and the restoration of capitalism.

The statement was by far the strongest issued by the Cuban Roman Catholic Church since Cardinal Jaime Ortega began a dialogue with Raúl Castro in 2010, which lead to the release of 115 political prisoners and its support for his reforms.

The Church issues such letters a few times a year.

Raúl Castro, since replacing his ailing brother Fidel as president in 2008, has embarked on the most significant reform of the Soviet-style system since the 1959 revolution, even while insisting the country's one-party political system was untouchable.

Last year former Pope Benedict said communism had failed in Cuba and offered the Church's help in creating a new economic model, drawing a reserved response from the Cuban government ahead of an official visit to the island.

The latest statement was delivered to the government before being read out in Cuban churches, Monsignor Jose Felix Perez, executive secretary of the Cuban Bishops Conference, told the media.

"The letter was read with the same spirit it was written ... constructively. With the desire for the improvement of peoples' lives," he said.

Cubans have expressed increasing frustration with the slow pace of reform and are emigrating in record numbers. Some have begun openly to question the political system through various Internet pages, a few connected to the Church.

"I want to elect the president through direct vote, and not another way," musician Robertico Carcasses said last week as he improvised a verse during a televised concert.

Carcasses and his jazz-fusion band were quickly sanctioned for the outburst, in which he also called for freedom of information while condemning U.S. sanctions.

CALL FOR RECONCILIATION

Since 2010 the Church has had more freedom to engage in public activities such as staging religious processions and offering adult education classes, as well as enjoying occasional coverage by official media.

Negotiations with the state over such issues as the return of confiscated property, the building of new churches and the opening of catholic schools, are ongoing, according to Church sources.

The bishops said that U.S. sanctions on Cuba and the more than half century of hostile relations between the two countries had "profoundly" affected Cubans' lives.

The letter quoted remarks by Pope John Paul II during a 1998 visit. "The forced isolation impacts the population indiscriminately ... The measures imposed from outside on the country are unjust and ethically unacceptable," the letter quoted the pope as stating.

(Additional reporting by Nelson Acosta; Editing by Cynthia Osterman)