"How long he stays on earth, that's a decision that will be made by the Almighty," Bush told foreign journalists Tuesday ahead of a weeklong trip to Latin America.
"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 live if that's what the people decide."
Castro is in failing health. For 47 years, he has had led a communist regime south of Florida's shores.
The Bush administration remains hopeful that his death will lead to grass-roots democratic reform, but so far, Castro's decision to transfer power to his younger brother, Raul, has gone seamlessly.
Bush said Cuba's future should not be based on the fact that "somebody is somebody's brother."
"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," Bush said. He was referring to the role that Latin American countries can play in leading Cuba to democracy.
"We believe the Cuban people ought to make the decision for the future," Bush said.
The U.S. cut off diplomatic ties with Cuba in 1961, two years after Castro led an armed revolution that drove out U.S.-backed dictator Fulgencio Batista. Decades-old trade and travel embargoes made it illegal for American businesses to trade in an economy they once dominated, and few Americans have visited Cuba.
Bush leaves Thursday on a trip to Brazil, Uruguay, Colombia, Guatemala and Mexico. The trip is aimed at showing Bush has not overlooked Latin America. He plans to focus on common agendas of trade, energy, and immigration.
The president said the trip will send a message to people in his own country, too. He said Americans must see the value of sending billions of their tax dollars elsewhere to help people in poverty get an education and health care.
"In a country where there are isolationist tendencies — where people sometimes say it's not our problem — the president has got to be constantly reminding people that poverty in our neighborhood is our problem," he said.
Bush covered a series of other topics in an interview with reporters from Central America and South America.
—Bush said that the model of government intervention championed by Hugo Chavez, Venezuela's leftist president, leads to higher poverty. The United States will bring a message of "open markets and open government" to the region, Bush said.
"Now, I fully recognize that until people actually feel progress in their pocketbook, that there's going to be frustrations with forms of government," Bush said. "But that doesn't mean you kind of revert to something that I don't believe will work."
—Bush stood by Colombian President Alvaro Uribe, who is dealing with a scandal involving ties between his political camp and brutal far-right militias. It has caused Congress to rethink the $700 million in aid the U.S. gives Colombia each year.
Bush said Uribe has assured him that investigations and prosecutions will be full and fair.
"In my judgment, President Uribe has done a fabulous job for leading that country," Bush said.
—Bush said he will use his visit to Mexico to tout the need for a new U.S. immigration policy. His approach, which runs at odds with some of his own party's leaders, calls for a guest worker program and a path to citizenship for illegal immigrants.
"It will help us dismantle an industry that has sprung up that uses human beings as product, as chattel," Bush said.
"Now the incentive is for people who want to do work that Americans aren't doing is to pay money, to be stuffed in the back of an 18-wheeler, for example, and driven across and ducked out in the desert, where they hope somebody will come and rescue them.... The industry that has sprung up as a result of the current immigration law is inhumane," Bush said.