President Abdelaziz Bouteflika is in full control of running Algeria, his premier said Monday in response to doubts raised by prominent public figures over the aging head of state's abilities.

"The president is supervising the implementation of his programme on a daily basis and step by step," Prime Minister Abdelmalek Sellal said on state television.

"State institutions must be respected," he said, calling for "an end to statements which provoke tensions in the country".

On Friday, a letter signed by 19 public figures was made public in which they warned of a "degradation of the general climate" in Algeria and asked to meet Bouteflika.

The signatories include former culture minister Khalida Toumi, 79-year-old senator Zohra Drif who fought against Algeria's French occupation, Trotskyist parliamentarian Louiza Hanoune and writer Rachid Boudjedra, as well as other supporters of the president.

Bouteflika has ruled the oil-rich North African state since 1999, but concerns have been growing over how much longer he can stay in power.

The 78-year-old won re-election last year but appeared only once during the campaign, in a wheelchair after suffering a stroke in 2013.

His public appearances have become rare, and he appears on local television only when foreign dignitaries visit.

His opponents, including his rival in the 2014 presidential polls Ali Benflis, have spoken of a "power vacuum".

"I know the president very well and I doubt that certain decisions were his initiative," said Toumi, who was in government from 2002 to 2014.

"We believe it is our duty as Algerian patriots to draw your attention to the degradation of the general climate in our country," she and the 18 others wrote in the letter.

The prime minister hit back, insisting that "the president of the republic is the sole constitutional guarantee of the continuity of the state and its stability".