Clearly struggling to speak, Abdelaziz Bouteflika, 68, addressed Algerians in an interview broadcast on state television shortly after leaving Val de Grace military hospital in Paris where he was taken for stomach bleeding.
"Are the Algerian people a little worried?" Bouteflika asked an interviewer from an unidentified Paris residence on Saturday.
Answering his own question, he said: "The people have no reason to be worried."
Flanking the president, Bouteflika's personal physician, Messaoud Zitouni, said he was "completely healed" after surgery that lasted "no more than an hour". He did not say when the operation had taken place.
Rumours about Bouteflika's health circulated after he was admitted to hospital on 26 November with an unspecified gastrointestinal problem.
The only statement published during Bouteflika's stay in hospital was a bulletin on 5 December that said he had undergone a successful operation for a bleeding stomach ulcer.
"The people have no reason to be worried"
Abdelaziz Bouteflika, Algerian president
"We have nothing to hide," Bouteflika said. "We have said everything in total clarity and in full transparency."
The president was initially admitted to a hospital in Algiers. Doctors advised him to be flown to Paris for thorough medical tests, a statement from his office had said.
"These tests showed an ulcer that required surgery," Dr Zitouni said. Such operations generally require 30 days of follow-up, he said, "we were fully in the norm".
In a statement announcing Bouteflika's release earlier on Saturday, Zitouni said the president's health was "evolving favourably," with "a very good prognosis".
Doctors advised "strict rest" before he resumes his official duties, the statement said.
King Mohammed VI of neighbouring Morocco, which has had tense relations with Algeria, notably over Moroccan-controlled Western Sahara, expressed "great satisfaction" that Bouteflika had left the hospital.
In a message to Bouteflika made public by the royal palace in Rabat, the Moroccan capital, the king expressed his "sincere feelings of cordiality, sympathy and great esteem".
Bouteflika was re-elected for a second term in April 2004. Government aides said this was his first hospitalisation since he took office in 1999.
Morocco's King Mohammed sent
his best wishes toBouteflika
Zitouni, in a playful tone, said that Algerians had "impatiently" awaited Bouteflika's return and had "missed the speeches" - an apparent reference to the president's reputation for long-winded addresses.
The president said: "God willing, if we remain healthy, we will give them a few more."