The move marked the first time Castro, two weeks away from his 80th birthday, relinquished authority in his 47-year rule.
The response in the communist country and elsewhere was mixed.
Some government work centers called for workers to gather to show their support for the leader. At one such gathering, workers shouted "Long live Fidel!" and waved small Cuban flags, reported the Associated Press.
Activist Manuel Cuesta Morua, however, said the move marks the start of a transition to a more collaborative government. "This gives Cuba the opportunity to have a more rational leadership because ... the top leaders will be obligated to consult each other."
In Miami, U.S. Rep. Lincoln Diaz-Balart and Cuban exile leaders called on pro-democracy activists inside Cuba to take to the street to protest the transfer of rule to Raul Castro.
''It's time for the military not to shoot'' at those who mount peaceful protests, Diaz-Balart said, according to the Miami Herald.
Raul Castro, 75, the country's defense minister and constitutional successor, has reportedly had a more public profile in recent weeks but did not come out with a statement about the temporary transition.
Castro, who took control of Cuba in 1959 and resisted U.S. attempts to oust him from power, last appeared in public at a July 26 event, where he appeared thin and weary during two long speeches, according to the AP.
On Monday, before news of Castro's illness, President Bush spoke about the island nation to a Miami radio program.
"If Fidel Castro were to move on because of natural causes, we've got a plan in place to help the people of Cuba understand there's a better way than the system in which they've been living under," he said.
A U.S. presidential commission three weeks ago proposed an $80 million program to bolster nongovernmental groups in Cuba to help bring an end to Cuba's communist system.
Castro's surgery was scheduled to repair a "sharp intestinal crisis with sustained bleeding," according to a statement from Castro.
"The operation obligates me to undertake several weeks of rest," he wrote.