Bouteflika, 76, was flown to Paris for treatment about three weeks ago following a mini-stroke and speculation has been rife about the state of his health.
French authorities said on Tuesday he been transferred from the Val de Grace military hospital in Paris to a new facility "to continue his convalescence" following treatment.
Algerian authorities broke official silence on Bouteflika's health on Monday, confirming he was recovering in Paris and saying his life was "never in danger."
In Algiers, Prime Minister Abdelmalek Sellal said on Wednesday the president is "doing well and resting."
And in a reference to speculation over Bouteflika, he said "there is not need to publish a daily bulletin about his health."
The secrecy surrounding his treatment in France led many in Algeria to speculate about the health of the president, who has ruled the country since 1999.
Authorities have denounced "false information" about his health and insisted Bouteflika has been keeping track of government activities.
Sellal repeated that people "should not believe" what certain foreign television channels say.
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