The Algerian president has undergone medical checks at a top French military hospital.
Senior Algerian politicians have told local media recently that Bouteflika has been well.
Analysts say the health of the 69-year-old president, who has sought to bring peace to the giant oil-exporting country of 33 million since taking office in 1999, is a critical factor in the political stability of Africa’s second-largest country.
No more questions
Answering a question after his meeting with Sarkozy, he said: “It’s true that I was very ill, but today I am much better.”
He then told reporters to “stop asking questions about my health”.
The subject of France was dealt with in a similarly frank manner.
Bouteflika met Sarkozy for a four-and-a-half-hour meeting, but made little effort to patch up differences with Algeria’s former colonial ruler.
“It’s fully clear that we [France and Algeria] are condemned to having a common future. We can do nothing about the laws of geography,” which place France and Algeria on opposite sides of the Mediterranean, he said.
Asked whether he could offer a word that could bring Algeria and France closer, Bouteflika said: “In these circumstances, I cannot say anything.”
Sarkozy’s two-day trip to Algeria had been encouraged by the French president, Jacques Chirac, and was billed as a chance to get bilateral ties back on track.
For Sarkozy,who is aiming to be the centre-right’s candidate for next year’s presidnetial election, the visit was steeped in political importance because roughly three million people of Algerian descent live in France.
On Monday, Sarkozy announced that the so-called Schengen zone nations of Europe will no longer consult one another before issuing visas to Algerians.
The move is expected to reduce the waiting time for Algerians seeking visas from about 15 days to between one and three days.