Speaking in a televised address after commandos killed the three gunmen responsible for the wave of terror, Hollande hailed the "courage" of French security forces -- but said France "has not finished with the threats targeting it".
Prime Minister Manuel Valls, speaking separately to a television channel, said, "We are confronting an unprecedented terrorist challenge." Valls said of this week's violence, "There will be a before and an after of what happened."
Paris has been on its highest state of alert since Wednesday when two of the gunmen stormed the offices of the Charlie Hebdo satirical newspaper, killing 12 people.
Fears of a jihadist campaign took hold the next day when a policewoman in a southern Paris district was murdered in the street by a third gunmen.
Yesterday, events came to a climax with two hostage-takings, in Paris and in a town to the northeast by
the gunmen. French commandos simultaneously stormed both sites, killing the men.
Hollande called the hostage-taking in Paris, which took place in a Jewish supermarket in the capital's east, "an appalling anti-Semitic act". More than a dozen people held by the gunman were freed after the commando raid, but four others died.
He also called for public vigilance and unity.
The horrific wave of violence elicited statements of sympathy and support for France from around the world. On Sunday, a mass rally to honour the dead and condemn the week's violence is planned in Paris. Hollande said he would attend the rally, together with several foreign leaders, including
the leaders of Germany, Britain, Spain and Italy.
Valls, meanwhile, vowed the government would investigate the events of the week to answer several "legitimate" questions. Among them how the gunmen who were known to the police, and two of whom were on a US no-fly list could mount such operations.
"We owe a duty of truth to the victims, to their families, and to our compatriots," he said.