"Our great and beautiful France will never break, will never yield, never bend" in the face of the Islamist threat that is "still there, inside and outside" the country, said Hollande.
The country has been shaken to its core by the bloodshed that began with a jihadist assault on the satirical Charlie Hebdo magazine on Wednesday and ended in a bloody hostage drama at a Jewish supermarket two days later.
Seventeen people, including journalists, policemen, a black police woman, Muslims and Jews lost their lives in the attacks.
The supermarket killer, Amedy Coulibaly, and the Charlie Hebdo gunmen, Said and Cherif Kouachi, were killed in quick succession in two police blitzes on Friday.
Refusing to be cowed by the attack that decimated its editorial team, Charlie Hebdo prepared a cover for its next edition Wednesday showing a weeping Prophet Mohammed holding a sign with the now-famous phrase "Je suis Charlie" under the banner "All is forgiven".
It is the kind of goading content that has long drawn the ire of some Muslims because of the depiction of Mohammed, which many see as sacrilegious.
French Muslim groups urged their communities to "stay calm and avoid emotive reactions" to the new Charlie Hebdo cover, while respecting freedom of opinion.
In Israel, thousands of mourners gathered at a cemetery for the funeral of Yoav Hattab, 22, Philippe Braham, 45, Yohan Cohen, 23, and Francois-Michel Saada, 64, who were killed at the kosher supermarket.
Israeli Prime Minister Benjamin Netanyahu told mourners that world leaders were "starting to understand that this terror committed by extremist Islam represents a clear and present threat to peace in the world in which we live."
During their attack on the magazine, which also lampoons other religions, the gunmen proclaimed they were "avenging the Prophet".
Charlie Hebdo, which has become the symbol of freedom of expression in the wake of the bloodshed, was preparing a massive print run of three million copies, compared to its usual 60,000.
Two policemen, Franck Brinsolaro, 49 and Muslim officer Ahmed Merabet, 40, were killed during the attack on Charlie Hebdo.
The third police officer Clarissa Jean-Philippe, 26, originally from the French Caribbean island of Martinique, was gunned down by Coulibaly the next day when she arrived on the scene of a car accident he was involved in in the southern suburb of Montrouge. Many believe he was on his way to a Jewish school down the road.
"That woman saved our children," said one parent.
At the Paris police headquarters pallbearers marched slowly through the square to the strains of a funeral march past a huge Tricolore flag fluttering lightly in the breeze.
"They died so that we could live in freedom," Hollande said of the police officers.
France has Europe`s largest Muslim and Jewish populations and the attacks prompted a historic outpouring of unity and saw nearly four million people rally across the country on Sunday.
Some 1.5 million came out onto the streets of Paris alone, but the nation remains jittery after its worst attacks in half a century and Defence Minister Jean-Yves Le Drian announced some 10,000 troops will be deployed to protect sensitive sites.
He said the deployment, in addition to another 5,000 police officers on the streets, was being handled like "a military operation".
"This is the first time that our troops have been mobilised to such an extent on our own soil," he said.
With tensions still high, Muslim community leaders have reported more than 50 incidents since the Charlie Hebdo assault, including apparent arson at a mosque in the city of Poitiers on Sunday.
Prime Minister Manuel Valls will on Tuesday address parliament on the country`s response to the terror threat as attention turns to security failings that allowed men known to anti-terror police to slip through the cracks.
Valls has admitted there were "clear failings" after it emerged that the Kouachi brothers had been on a US terror watch list "for years".
Said Kouachi, 34, was known to have travelled to Yemen in 2011, where he received weapons training from Al-Qaeda in the Arabian Peninsula. And 32-year-old Cherif was a known jihadist convicted in 2008 for involvement in a network sending fighters from France to Iraq.
The brothers carried out the Charlie Hebdo attack before leading security forces on a massive manhunt that ended at a small printing business outside Paris where they took the manager hostage.
Police gunned them down after they ran out of the building spraying bullets in a final act of defiance.
Coulibaly claimed he had coordinated his acts with the brothers.
The repeat criminal offender had also been convicted for extremist activity and swore allegiance to the Islamic State group.
As investigators hunted for those who may have assisted the killers, images of Coulibaly`s wanted partner Hayat Boumeddiene emerged at Istanbul airport accompanied by an unidentified man. She is believed to have entered Turkey before the attacks and went on to Syria.
"We think there are in fact probably accomplices," Valls told French radio. "The hunt will go on."
In Bulgaria it emerged a Frenchman arrested on January 1 trying to cross into Turkey was in contact with Cherif Kouachi.
France has been on high alert for several months over its citizens who go to fight alongside Islamic State jihadists in Iraq and Syria, some of whom have been pictured in grisly execution videos.
Valls also said 1,400 people were known to have left to fight in Syria and Iraq, or were planning to do so. Seventy French citizens have died there.
The IS group has issued direct threats against France which is carrying out air strikes against them in Iraq as part of a US-led coalition.
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