SFAX, TUNISIA -- A third suspect is in French custody Saturday in connection with an Islamic extremist knife attack that killed three people in a Nice church, as the distraught family of the suspected Tunisian assailant asked to see video footage of what happened.

Investigators in France, Tunisia and Italy are trying to determine the motive of chief suspect Ibrahim Issaoui, and whether he acted alone and whether he premeditated Thursday's attack on the Notre Dame Basilica.

Authorities have labeled the attack, which took place amid growing tensions around cartoons published by a French newspaper mocking the Prophet Muhammad, an act of Islamist terrorism.

Issaoui, who transited through Italy last month en route to France, is in critical condition in a French hospital after being wounded by police as they arrested him.

A 35-year-old man who had met with Issaoui in Nice was arrested overnight, a judicial official said Saturday. A 47-year-old man who had met with Issaoui the night before the attack was already in custody, bringing the number of detained suspects to three. Their connection to the attack remains unclear.

A previously unknown Tunisian extremist group claimed responsibility for the attack, and Tunisian and French authorities are investigating whether the claim is legitimate.

In Issaoui's hometown of Sfax, his family expressed shock and appealed for peace. But they also expressed bewilderment that this young man who drank alcohol and showed no outward signs of radicalism would flee to France and attack a church.

"We want the truth about how my son carried out this terrorist attack. I want to see what the surveillance cameras showed. I will not give up my son's rights outside the country. I want my son, dead or alive," his mother Gamra told The Associated Press, her words often interrupted by tears.

His father and brother Wissem said that if Issaoui indeed carried out the attack, he should face justice.

"We are Muslims, we are against terrorism, we are poor. Show me that my brother committed the attack and judge him as a terrorist," Wissem said. "If he was the attacker, he will take his responsibility."

On the dusty Tina Street, amid low-rise homes in the working class Nasr neighbourhood of Sfax, friends and neighbours said Issaoui sold gasoline for motorcycles and while not starving or homeless, he was poor like many in the area. That poverty is driving more and more young Tunisians to seek jobs and opportunity in Europe this year.

He had had small-time run-ins with the law as a teen, but nothing that alerted Tunisian authorities to possible extremist leanings. That meant that when he was served an expulsion order from Italy, he could go where he pleased.

Italy's interior minister, Luciana Lamorgese, told the AP that Italy's overburdened repatriation centres had no place for him.

"Obviously, we give precedence to people who are signalled by law enforcement or by Tunisian authorities," Lamorgese said. "The number of spots are not infinite, and he could not therefore be placed inside a repatriation centre."

A friend believed to have hosted Issaoui in Alcamo in western Sicily for a couple of weeks told police that Issaoui found work in the area for some days picking olives, then abruptly departed, Italian newspaper La Republicca reported Saturday. Police also searched the friend's home, Italian media reports said.

Meanwhile, anger at France remains high among many Muslims abroad over France's defence of the prophet cartoons and President Emmanuel Macron's pledges to crack down on Islamist fundamentalists.

Turkish President Recep Tayyip Erdogan, who has been at odds with Macron on several fronts lately, said Saturday: "All kinds of insults towards our prophet target all Muslims."

Indonesian President Joko Widodo, the leader of the world's most populous Muslim nation, on Saturday strongly condemned terrorist attacks in France as well as comments by Macron seen as offensive toward Islam.

The French Embassy in Jakarta issued a statement seeking to calm spirits, saying "there was no intention at all to generalize" and that Macron "clearly distinguished between the majority of French Muslims and the militant, separatist minority that is hostile to the values of the French Republic."

Macron himself gave an interview to broadcast network Al-Jazeera scheduled to air Saturday, and spoke with Pope Francis about the attack on the church and current religious tensions.

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Charlton reported from Paris. Trisha Thomas and Frances D'Emilio in Rome, Zeynep Bilginsoy in Istanbul and Niniek Karmini in Jakarta contributed.