The first pictures to emerge of Algeria's President Abdelaziz Bouteflika since he was hospitalised in France in April after a mini-stroke were published by state media on Wednesday.

Footage broadcast by Algerian television showed the 76-year-old sitting in an armchair drinking coffee as he conferred with Prime Minister Abdelmalek Sellal and army chief Ahmed Gaid Salah, who visited him on Tuesday in the Paris hospital where he is convalescing.

Earlier, photographs of Bouteflika wearing a dressing gown as he received the two officials were published by the APS news agency.

The pictures from the two-hour meeting were published to dispel rumours circulating in both Algiers and Paris about the president's condition deteriorating.

Sellal presented Bouteflika with an "exhaustive report on the general situation in Algeria and the government's activities", a presidency statement said.

The prime minister said the head of state had "responded very well and his health seemed fine", adding that he had given detailed instructions on running the country.

He said Bouteflika had instructed Sellal "to finalise the draft finance act for 2013 and all the other bills being considered by the government so that they are ready to be adopted at the next cabinet meeting".

The ageing president's latest health-related absence has prompted local media to increasingly question the implications for the government, given Bouteflika's central constitutional role in running Algeria.

It has also sparked intense discussion about next year's presidential election, now that it appears extremely unlikely he will seek a fourth term.

Calls have grown in the Algerian press for the application of Article 88 of the constitution, which provides for the transfer of power if the head of state falls seriously ill.

A letter published on Tuesday by one of the few surviving nationalist leaders who launched a war against French colonial rule in 1954 urged the army, which has always played a decisive if undefined role in Algerian politics, to act swiftly to end the leadership crisis.

"With the president now sick, the whole state is affected. These are the consequences of exercising power in a despotic way," Mohamed Mechati wrote in a letter to Le Soir d'Algerie newspaper, calling on the military to "act swiftly for the survival of our country".

The defence ministry responded on Wednesday by insisting that the army was a "national republican institution with missions clearly defined by the constitution" to defend the nation.

Bouteflika's health has been an endless source of speculation in Algeria since 2005 when he had surgery at the same Paris hospital for a bleeding stomach ulcer, according to officials, and spent a long period convalescing.

A leaked US diplomatic cable in 2007 suggested he might be suffering from terminal stomach cancer, and since being re-elected for a third term in 2009 he has rarely appeared in public or travelled outside Algiers.

Reflecting strenuous government efforts to reassure the public, a health bulletin was published by APS on Tuesday, in which the president's doctors in Paris "recommended that he observe a period of convalescence and functional rehabilitation to consolidate his recovery".

It said the transient ischaemic attack, or mini-stroke Bouteflika suffered on April 27, had "not affected his vital functions", and that he had been transferred to the Val de Grace hospital in Paris for further tests.

Bouteflika rose to power in 1999, and was re-elected in 2004 and again in 2009, after changes to the constitution allowed him to stand for more than two terms.

Before his latest hospitalisation, and despite his age and already frail health, some supporters were urging the Algerian leader to seek a fourth mandate in next year's presidential election.