His trip comes after Libya's internationally recognised government said the jihadist mastermind of the 2013 siege of an Algerian gas plant in which 38 hostages died had been killed in a US air strike.
Speaking to reporters in Algiers, Hollande acknowledged the attack that killed Mokhtar Belmokhtar, saying France and Algeria were waging a "common battle... Against this terrible, implacable enemy which we have targeted and again recently in the past few hours".
"We discussed all the international questions," including "the situation in the Sahel, the battle against terrorism and what happened in Chad (where 23 people were killed in suicide bombings Monday), Mali and Libya," Hollande said after the meeting.
He added that his talks with Bouteflika should "reinforce ties" between France and Algeria on "the economic, cultural and human levels".
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Hollande, who met separately Prime Minister Abdelmalek Sellal, said at the start of his visit that "France is Algeria's first trade partner and expects to further boost its presence... With the installation soon of important companies such as Renault, Sanofi, Alstom and Peugeot."
Mutual concern over rampant jihadism in North Africa has brought the former foes closer together in recent years.
Algeria shares a border with Mali's north, which is still fragile after a French-led operation in 2013 ousted jihadists who had seized the upper half of the west African nation.
While French troops patrol northern Mali, Algiers has mediated a peace accord between Mali's main Tuareg-led rebel groups and Bamako which will be signed on June 20.
Algeria has also hosted talks between rival political factions from chaos-torn Libya, with which it also shares a long border.