He was admitted to the Geneva University Hospital (HUG) on February 24 for "periodic medical examinations", according to the Algerian presidency.
Algerian President Abdelaziz Bouteflika on Sunday returned home after a two-week stay in Switzerland's Geneva for "routine medical checks", confirmed a statement by the President Office.
Army Chief of Staff Ahmed Gaid Salah added his voice, saying Sunday that the army and the people "have the same vision of the future".
The president has said the demonstrations could plunge the country into "chaos". Protests also were held in neighbouring Rabat, Morocco.
The recent protests surprised Algeria's opaque leadership and freed the country's people, long fearful of a watchful security apparatus, to openly criticize the president.
The protests trickled down to middle-schoolers and high-schoolers, with several hundred marching in the center of Algiers, also calling for Bouteflika to withdraw his candidacy.
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Rashida Tlaib, D-Mich., marched on Capitol Hill with impeachment supporters, and Rep. She added: " And he's just not worth it ". Other Democrats are more enthusiastic.
Political sources said the military would nearly certainly play a leading role in Algeria's transition process, and are already assessing three or four civilian figures who could be suitable for the presidency. "This will be a sleepless night", said 25-year-old Abdelghani Hachi.
He became president in 1999 and reconciled a nation riven by a deadly Islamic insurgency, but questions swirl over whether he is really running the country today. He was deposed in a bloodless military coup in 1965 that set the stage for a series of generals serving as presidents.
Over the past few weeks, tens of thousands of people from all social classes have been demonstrating nearly daily against Bouteflika's decision to stand in the election, rejecting a stale political system dominated by veterans of an independence war against France that ended in 1962.
But he held a tight rein on the country and his government was unable to create jobs, despite a massive investment drive through the 2000s paid for by exploiting large reserves of oil, gas and other natural resources.
An Algerian government plane, hidden from view in a hangar, was reported to have left Geneva around 1500 GMT.
Algerian officials had said days ago that Bouteflika was expected to return shortly.