(Adds Bush interview on CNN)

By Steve Holland

WASHINGTON, March 7 (Reuters) - Communist rule of Cuba should end when ailing leader Fidel Castro dies, U.S. President George W. Bush said as he prepared for a Latin American tour seen as aiming to counter a regional shift to the left.

Bush's trip, starting in Brazil on Thursday, is widely viewed as offering a counterpoint to the populist appeal of Venezuelan President Hugo Chavez, whose nationalization plans he criticized.

"I strongly believe that government-run industry is inefficient and will lead to more poverty," Bush told newspaper reporters on Tuesday in remarks released on Wednesday.

"If the state tries to run the economy, it will enhance poverty and reduce opportunity."

Bush also made clear he is keeping an eye on Cuba and its long-time leader.

Castro, 80, was forced to temporarily hand power to his brother, Defense Minister Raul Castro, last July after stomach surgery. He has not appeared in public since his surgery, aside from video recordings and a live radio broadcast to Venezuela last week.

Castro's fate will be decided "by the Almighty," Bush said.

"I don't know how long he's going to live but nevertheless I do believe that the system of government that he's imposed upon the people ought not to live if that's what the people decide."

Bush took a dim view of the possibility of Raul Castro taking over permanently.

"What I hope happens is that we together insist that transition doesn't mean transition from one figure to another, but transition means from one type of government to a different type of government, based upon the will of the people," he said.

SOFTER MESSAGE

Bush's six-day tour will include visits to Brazil, Uruguay, Colombia, Guatemala and Mexico.

He takes a message aimed at improving his reputation and bolstering U.S. influence in a region where anti-American voices like Chavez's are rising.

"I bring a message of hope," Bush said.

"The trip really is to remind people that we care," Bush told CNN's Spanish language channel on Wednesday. "I do worry about the fact that some way, well, the United States hasn't paid enough attention to us, or the United States really isn't anything more than worried about terrorism."

Bush avoided mentioning the fiery Venezuelan leader's name, particularly when asked about Chavez's plans to hold a protest rally in Argentina while he is in neighboring Uruguay.

Pushing free trade and open markets, Bush rejected the development model championed by Chavez that calls for nationalization of industry and greater government intervention.

"I fully recognize that until people actually feel progress in their pocketbook that there's going to be frustrations with forms of government. But that doesn't mean you kind of revert to something that I don't believe will work," he told the newspaper reporters. (Additional reporting by Matt Spetalnick)

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