The suspect is reported to have been arrested and taken to hospital after being injured as police intervened.
Three people were killed and several others injured in what French President Emmanuel Macron said was an "Islamist terrorist attack".
A man armed with a knife attacked church-goers in the French city of Nice.
Macron said following the attack that the number of soldiers deployed to protect schools and religious sites would be doubled, to 7,000. The French government has raised its security alert level to its maximum level.
The attack comes just 12 days after a teacher was beheaded in the Paris suburbs and on the eve of a second lockdown across France due to the coronavirus pandemic.
Authorities said the attack took place inside Notre-Dame basilica in the heart of Nice's old city and that the attacker was shot and wounded. He was taken to hospital.
France’s anti-terrorism prosecutor, Jean-Francois Ricard, said a man and woman were killed inside the church. The third victim, a 44-year-old woman who managed to flee, died at a nearby restaurant.
A 60-year-old woman whose body was found at the entry of the church, suffered “a very deep throat-slitting, like a decapitation,” Ricard added. The 55-year-old man also died after deep cuts to his throat.
The attacker is believed to have shouted "Allah Akbar" as he carried out the assault, according to an unconfirmed claim from a police source.
Nice's mayor has said the man continued to shout the words as he was tackled by police.
An investigation has been opened for murder and attempted murder in connection with a terrorist enterprise - a common term for such crimes.
What do we know about the suspect?
France’s anti-terrorism prosecutor Ricard, said the attacker, who was born in 1999, was not on the radar of intelligence agencies as a potential threat.
He added the man was a Tunisian who entered France from Italy. The travel information came from a document from the Italian Red Cross, Ricard said.
A copy of the Qur'an - the Muslim holy book - and two telephones were among the things found on the attacker, according to the prosecutor, as well as the knife used in the attack, which had a 17-centimetre blade. A bag with his personal affairs was found to contain another two unused knives.
Macron - 'We will not yield'
Macron travelled to Nice after presiding over a government crisis meeting on Thursday, and France's anti-terror prosecutors have launched a murder inquiry which will be carried out by judicial police and internal security investigators.
Talking to reporters in Nice, Macron urged French people to "not give in to the spirit of division".
"Once again our country has been hit by an Islamist terrorist attack. Once again this morning, three of our compatriots fell in Nice in this basilica Notre Dame. Quite clearly, it is France which is attacked."
"At the same time, we had a French consular site which was attacked in Saudi Arabia in Jeddah, and arrests on our territory were being made.
"If we are being attacked once again it is for the values that are ours, for our taste for freedom, for this possibility on our soil to believe freely and not give in to any spirit of terror," he continued, adding: "we will not yield to it."
Security alert raised to the maximum across France
French Prime Minister Jean Castex has raised the security alert to the maximum level for the whole of France and all churches in Nice have been closed until further notice.
Tensions have risen recently between France and parts of the Muslim world in a resurgence of the long-running clash over freedom of expression and secular values relating to cartoons of the Prophet Muhammad.
Separately, a man armed with a pistol and reportedly threatening police was shot dead by officers in Avignon, also in southern France. Police say no-one else was hurt and there was no evidence "at this stage" of an Islamist attack.
In Saudi Arabia, a security guard at the French embassy was stabbed by a man who was then arrested, the embassy said in a statement. The guard was injured and taken to hospital but his life is not said to be in danger.
Scenes of panic around Notre Dame
In Nice, Daniel Conilh, a 32-year-old bar worker serving in a nearby café, described the scene as it unfolded.
"Everyone ran away, there was shooting. A woman came straight out of the church saying to us: 'run, run, someone has gone down, there's going to be shooting, people are dead'," he recounted, adding that he called for calm as panicked customers fled the café.
Several police officers and other emergency workers quickly intervened, reports say. Police later said the situation was under control and there was no need to panic.
Church bells tolled across France at 3pm to mark the atrocity and show respect for the victims.
Nice mayor blames 'Islamo-fascism'
Nice Mayor Christian Estrosi was among the first to give details of the attack on social media. "I confirm that everything suggests this was a terror attack," he added.
"Enough is enough, it is now time for France to exempt itself from laws on peace to wipe out Islamo-fascism once and for all from our territory," Estrosi added.
Turkey's 'solidarity with people of France'
Condemnation also came from religious group, both Christian and Muslim, on Thursday.
"I can only strongly condemn the cowardice of this act against innocent people," said Abdallah Zekri of the French Council of the Muslim Faith (CFCM) in a statement.
The Vatican released a statement saying the Pope was "praying for the victims".
The French Bishops' Council (CEF) said they were stunned by an "unspeakable" act, adding that they hoped "Christians do not become a target for slaughter".
"This gangrene which is terrorism must be fought urgently, in the same way that there is an urgent need to install fraternity in our country in a concrete manner," said spokesman Hugues de Woillemont.
The Turkish Foreign Ministry "strongly condemned" the attack in a statement, offering its "condolences to the relatives of the victims".
A spokesman for President Recep Tayyip Erdogan tweeted his condolences in Turkish and French. "We will fight all kinds of terror and extremism with determination and in solidarity," Ibrahim Kalin said.
Tensions between France and Turkey have escalated over the past few days with Erdogan denouncing Macron, accusing him of leading a "hate campaign" against Islam. France recalled its ambassador to Ankara in retaliation.
Macron had spoken out on freedom of expression after a teacher was beheaded by a teenage radical Islamist nearly two weeks ago. Samuel Paty had shown caricatures of the Prophet Muhammad in class discussions.
Relations between the two countries had already been tense over Syria, Libya and the eastern Mediterranean.
The head of the European Council, Charles Michel, tweeted to express his solidarity with France and the French people. "The whole of Europe is with you," he said.
European Commission President Ursula von der Leyen also took to Twitter to condemn "the odious and brutal attack", adding that Europe was united with France against "barbarity and fanaticism".
German Chancellor Angela Merkel said she was "deeply shocked", and her thoughts were with the victims' relatives, a German government spokesman posted on Twitter.
British Prime Minister Boris Johnson said in a tweet in French that he was "shocked" by the "barbaric attack".
"I was shocked to learn the news of the barbaric attack in the Notre-Dame basilica in Nice. Our thoughts are with the victims and their families, and the UK stands alongside France in the fight against terror and intolerance," he wrote.
Other messages of support included wishes from the European Parliament President David Sassoli, and the Italian Prime Minister Giuseppe Conte.
The south-eastern French coastal city has already been hit hard by terrorism. More than 80 people died and nearly 500 were injured in Nice on Bastille Day in 2016 when an Islamist terrorist ploughed a truck through crowds gathered on the Promenade des Anglais to watch fireworks.
The three who died in Nice bring to 260 the number of people in France killed in terrorist attacks since 2015, according to an AFP tally.