A major manhunt has been launched for gunmen who shot dead 12 people at the Paris office of the French satirical magazine Charlie Hebdo.
Eight journalists and two policemen were among the dead. Police issued photos of two suspects, describing them as "armed and dangerous".
A third suspect reportedly handed himself in to police.
Protests and vigils over the attack, the deadliest the country has seen in decades, have been held across France.
President Francois Hollande called it a "cowardly murder" and declared a day of national mourning on Thursday.
He said the country's tradition of free speech had been attacked and called on all French people to stand together. "Our best weapon is our unity," Mr Hollande said in a televised address late on Wednesday.
Security has been stepped up across France in the wake of the attack, with Paris placed on the highest alert.
Police said arrest warrants had been issued for Cherif Kouachi, 32, and his brother Said, 34, who they said were believed to be "armed and dangerous".
Another suspect, Hamyd Mourad, 18, was named earlier in a police document, according to media reports.
However, unnamed officials said that Mr Mourad handed himself in to police after seeing his name circulating on social media. He was arrested and taken into custody, AFP reported.
Media reports described Cherif Kouachi as a militant sentenced in 2008 to three years in prison for belonging to a group sending jihadist fighters to Iraq.
BBC Paris correspondent Lucy Williamson says there are separate reports of police operations taking place outside the capital and in the eastern city of Reims, 140km (90 miles) from Paris.
Police did not give any details but forensic teams were later seen searching an apartment in Reims.
The satirical weekly has courted controversy in the past with its irreverent take on news and current affairs. It was firebombed in November 2011 a day after it carried a caricature of the Prophet Muhammad.
The attack took place as the magazine was holding its weekly editorial meeting. French media have named three cartoonists killed in the attack as Cabu, Tignous and Wolinski, as well as Charlie Hebdo contributor and French economist Bernard Maris.
Charlie Hebdo editor Stephane Charbonnier, 47, had received death threats in the past and was living under police protection.
Cartoonist Corinne Rey, said the hooded gunmen entered the building after forcing her to enter the code to open the door.
"They said they belonged to al-Qaeda," she said, adding they had spoken in fluent French.
Eyewitnesses said they heard as many as 50 shots fired by the attackers both inside the Charlie Hebdo office and on the streets outside.
The gunmen were captured on amateur video shooting one injured police officer at point blank range in the head on the pavement outside.
They were heard shouting "we have avenged the Prophet Muhammad" and "God is Great" in Arabic ("Allahu Akbar").
Police said the masked gunmen fled to northern Paris, before abandoning their car and hijacking a second one.
The Paris prosecutor, Francois Molins, said 11 people had been wounded in the attack, four of them seriously.
He told reporters all efforts were being made to find those responsible, without giving any details about the investigation.
"The investigations have been numerous and in-depth, because of course, the police have been mobilised, and these inquiries are going on."
The killings have been condemned by leaders worldwide, with US President Barack Obama offering to help France track down those responsible.
Al-Azhar University in Cairo, Sunni Islam's leading centre of learning, called the attack "criminal" and said "Islam denounces any violence".
The Arab League also condemned the attack. Pope Francis called it "abominable".
Thousands of people have gathered at the Place de la Republique in central Paris for a vigil, many holding up placards saying "Je suis Charlie" (I am Charlie), referring to a hashtag that is trending on Twitter in solidarity with the victims.
Piles of pens - symbolising freedom of expression - and candles have been laid across the square.
Tens of thousands of people have also joined rallies in other cities across France.
Charlie Hebdo's website, which went offline during the attack, is displaying the single image of "Je suis Charlie" on a black banner. Other major newspapers are displaying similar banners.
The latest tweet on Charlie Hebdo's account was a cartoon of the Islamic State militant group leader, Abu Bakr al-Baghdadi.
Analysis: Hugh Schofield, BBC News, Paris
Charlie Hebdo is part of a venerable tradition in French journalism going back to the scandal sheets that denounced Marie-Antoinette in the run-up to the French Revolution.
The tradition combines left-wing radicalism with a provocative scurrility that often borders on the obscene. Its decision to mock the Prophet Muhammad in 2011 was entirely consistent with its historic raison d'etre.
The paper has never sold in enormous numbers - and for 10 years from 1981, it ceased publication for lack of resources.
But with its garish front-page cartoons and incendiary headlines, it is an unmissable staple of newspaper kiosks and railway station booksellers.
The country was already on the alert for Islamist militant attacks after several incidents just before Christmas, although the French government has denied the attacks were linked.
It is the deadliest attack in France since 1961, when a bomb planted by far-right militants opposed to plans for Algerian independence killed 28 people on a train.
Danish newspaper Jyllands-Posten, which published cartoons of the Prophet Muhammad in 2005 sparking riots in Muslim countries, says it has stepped up security in the wake of the Charlie Hebdo attack.