France has announced it will tighten security around transport and public places following the killing of a French hostage by jihadists in Algeria.
It will also boost its support for Syrian opposition forces fighting Islamic State (IS) militants.
The move was announced by the office of President Francois Hollande after a high-level emergency meeting.
Militants allied to IS killed French tourist Herve Gourdel after demanding that France halt air strikes on IS.
Islamic State has seized large areas of Syria and Iraq in recent months.
French warplanes have been taking part in US-led air strikes against IS in Iraq since last Friday, and on Thursday they carried out new raids.
However, France has so far refrained from joining the US and several Arab states in attacking targets in Syria.
'Never cede to terrorism'
Before the emergency meeting took place, Defence Minister Jean-Yves Le Drian told French radio that France would consider targeting IS in Syria as well as Iraq.
Mr Le Drian said it was "a question that is on the table". But he added: "The opportunity is not there today. We already have an important task in Iraq."
After the killing of Mr Gourdel, 55, President Hollande said that French strikes in Iraq would continue.
"France is going through an ordeal through the murder of one of its citizens, but France will never give in to blackmail," Mr Hollande told the UN General Assembly on Wednesday.
"The fight against terrorism must continue and be stepped up."
Speaking on the sidelines of the assembly, he said that Mr Gourdel - who was seized on Sunday - had been killed because he was a representative of French people who "defend human dignity against barbarity".
"France will never give in to terrorism because it is our duty, and, more than that, because it is our honour.''
Several French cities, including Mr Gourdel's home city in Nice, had flags flying at half mast on Thursday.
A government spokesman said flags across the country would be lowered over the weekend.
The head of the French Council of the Muslim Faith called on fellow Muslim leaders to meet on Friday to condemn militant attacks carried out in the name of Islam.
The Algerian militants Jund al-Khilafa (Soldiers of the Caliphate) posted a video on Wednesday of Mr Gourdel's murder, entitled "Message of blood for the French government".
IS itself has beheaded three Western hostages since August: US journalists James Foley and Steven Sotloff, and British aid worker David Haines. Their deaths were all filmed and posted online.
The group has also threatened to kill Britain's taxi driver Alan Henning, who was seized while on an aid mission to Syria in December.
French and Algerian newspapers react to murder
"Executed for being French," says French daily Liberation, framing his photo in black on its entire front page. "Murdered," is the headline in La Depeche du Midi.
France is now "plunged into fear", says Cecile Cornudet in Les Echos, adding: "It's the role of a political leader to stop that fear from turning into panic."
Dominique Quinio, in Catholic newspaper La Croix, says the French authorities are not to blame but "those who have decided that those who don't think or live like them…no longer have a place on Earth".
In Algeria, state-owned daily Ech-chaab calls the murder "a cowardly action and a hideous crime".
The entire front page in privately-owned daily Al-Fadjr carries the headline: "The return of brutality?!"
Mr Gourdel worked as a mountain guide in the Mercantour national park in the Alps.
He had also been organising treks through the Atlas Mountains of Morocco for some 20 years, and had also visited Nepal and Jordan.
In the video posted by his killers, he is shown on his knees with his hands behind his back in front of four masked, armed militants.
He is allowed briefly to express his love for his family before one of the militants reads out a speech in which he denounces the actions of the "French criminal crusaders" against Muslims in Algeria, Mali and Iraq.
The beheading, the spokesman says, is to "avenge the victims in Algeria... and support the caliphate" proclaimed by IS in Iraq and Syria.
In Nice, residents expressed their horror over the killing.
"It's a terrible shock," Deputy Mayor Christian Estrosi was quoted as saying by the AFP news agency.
He added that Mr Gourdel's family had reacted to his death "with dignity, anger and an unspeakable pain".
Who are Jund al-Khilafa?
- Previously part of al-Qaeda in the Islamic Maghreb (AQIM), which grew out of Algerian Islamist groups involved in 1990s civil war
- Carried out numerous attacks in Kabylie region - in April, ambushed an army convoy, leaving 11 soldiers dead
- Many residents have fled the region's forests and mountains in recent years because of insecurity
- Group said to be led by Abdelmalek Gouri, known as Khaled Abou Slimane, 37
- On 14 September, pledged allegiance to Islamic State