“This is an important page in the history of Algeria that turns,” Mr Le Drian said. “We are confident in the ability of all Algerians to continue this democratic transition in the same spirit of calm and responsibility.”
US State Department spokesman Robert Palladino said: “Questions about how to navigate this transition in Algeria, that is for the Algerian people to decide.”
Earlier on Tuesday, army chief of staff Lt Gen Ahmed Salah said he was on the side of the people and that no more time should be wasted in replacing the president.
On Monday the president, who is in poor health, said he would step down by the end of the month after 20 years in power.
The military dismissed Mr Bouteflika’s promise to resign before his term ends on April 28, saying it was time to invoke constitutional articles that would allow for him to be declared unfit for office.
Once a close ally of Mr Bouteflika, Gen Salah first broached the possibility of impeachment last week. He said the army’s move had been met with foot-dragging and deceit.
“We see no room for any more procrastination,” he said.
Meanwhile, protests continued in Algiers by students demanding a new generation of rulers, suggesting Mr Bouteflika’s promise to resign by the end of the month had not reduced public pressure for an end to his rule.
“We want a regime change” and “We don’t want Bouteflika or Said [his brother and presidential adviser]”, the crowd chanted.
Former prime minister Ali Benflis was among the leading voices against any delay to Mr Bouteflika’s resignation because it would leave the country’s secretive, distrusted power structure in place.
Protests have been driven by youths demanding the removal of a ruling elite seen by many as out of touch with ordinary Algerians and unable to revive an economy riven by cronyism.
Mr Bouteflika at first sought to defuse the unrest by saying on March 11 he was dropping plans to run for a fifth term.
But he gave no time for his exit, advocating a national conference on reforms to address the outpouring of discontent over corruption, nepotism and economic mismanagement.
Mr Bouteflika’s hesitation further enraged protesters.
Most opposition parties have rejected a caretaker government named by Mr Bouteflika on Sunday because they consider new Prime Minister Noureddine Bedoui as too close to the ruling elite.
Some demonstrators have rejected Algeria’s tradition of military intervention in civilian matters and want to dismantle the entire power elite, which includes army officers, the long-ruling National Liberation Front party, business tycoons and union leaders.
Several close allies, including party figures and union leaders, have in the past weeks abandoned Mr Bouteflika.
Meanwhile, prosecutors said they had banned corruption suspects from leaving Algeria after launching investigations into corruption and illegal money transfers by unidentified people.
The ban followed the arrest of the president’s key backer, businessman Ali Haddad.
Mr Haddad, described by Forbes magazine as one of Algeria’s wealthiest entrepreneurs, was detained overnight on Saturday at a border post with neighbouring Tunisia.
On Sunday, Algerian authorities also banned all private aircraft from taking off and landing until the end of the month.