PARIS — Prime Minister Manuel Valls on Saturday declared France was at “war” with radical Islam after three days of bloody attacks in and around Paris that sparked fears of a tide of violence by terrorists living in Europe.

French leaders called for their nation to turn out Sunday in support of victims of the brazen attacks that paralyzed the country.

Authorities said they would deploy thousands of police officers and soldiers to secure the nationwide rallies, in a marker of the newfound sense of vulnerability and fear that has struck this diverse country proud of its history of tolerance.

French President François Hollande convened his top security advisers Saturday, a sign of the deep-seated worry about further violence.

Authorities were still searching for Hayat Boumeddiene, 26, the partner of the man suspected in the slayings of a police officer Thursday and four more people at a kosher grocery store Friday. Those actions occurred just after a rampage allegedly carried out by his associates that left 12 dead at the offices of a satirical newspaper that had published cartoons mocking Islam.

By Saturday evening, French security officials said they thought that Boumeddiene had fled to Turkey on Jan. 2 and that she might have gone to Syria on Thursday, the day her partner killed the police officer.

The Syrian connection raised questions about the assailants’ ties to Islamist terrorist groups.

Boumeddiene’s partner, Amedy Coulibaly, said Friday that he had organized his attacks in conjunction with the Islamic State, a brutal terrorist organization that controls large portions of Syria and Iraq. Thousands of native-born European citizens are thought to have slipped into Syria to fight in the civil war.

France is in a “war against terrorism, against jihadism, against radical Islamism, against everything that is intended to break fraternity, liberty, solidarity,” Valls told an audience in Evry, a town south of Paris.

Law enforcement officials pledged Saturday to hunt down Boumeddiene, a French native they think had trained alongside her partner.

“We will do everything in our power to find her,” said Christophe Crepin, a senior police official. He vowed that she would not escape French law enforcement even if she were in Syria. “We are at war, and we will take the necessary measures,” he said.

Many French leaders emphasized the scale of the fight ahead of them, even as profound questions were raised about the future of France’s status as a tolerant, multicultural nation. Muslims have long had a vibrant presence here, a legacy of France’s colonial involvement in Africa and the Middle East, but a far-right, anti-immigrant party was topping some polls even before the attacks.

Valls and other French leaders have discouraged the National Front Party from taking part in Sunday’s rallies. But party leader Marine Le Pen hit back forcefully Saturday, saying, “We will not submit to the brutality of those who exclude us from the nation.”

She called on supporters to participate in gatherings elsewhere.

It was unclear what role Boumeddiene played in the attacks that started Wednesday, when brothers Cherif and Said Kouachi are alleged to have opened fire at the offices of the Charlie Hebdo newsweekly.

In two locations outside Paris on Friday, Coulibaly and the Kouachi brothers were killed.

On Saturday, French Interior Minister Bernard Cazeneuve said that the country remained on the highest security alert. The leaders of Britain, Germany, Italy, Spain, Israel and other countries planned to attend the Sunday rally in Paris. The United States was sending Attorney General Eric Holder. Turkish Prime Minister Ahmet Davutoglu also said he would attend, making him the highest-profile official from the Muslim world.