(Changes day in lead)
* France at war with Islamist ideology - minister
* Country on high security alert after Nice church attack
* Thousands of Muslims protest in Bangladesh
* Macron says he will not give ground on freedoms
By Tangi Salaün
PARIS, France, Oct 30 (Reuters) - France's interior minister said on Friday more militant attacks on its soil were likely and the country was engaged in a war against Islamist ideology following the second deadly knife attack in its cities in two weeks.
Minister Gerald Damarnin was speaking a day after an assailant shouting "Allahu Akbar" (God is Greatest) beheaded a woman and killed two other people in a church in Nice. The man was shot by police and is now in critical condition in a hospital.
"We are in a war against an enemy that is both inside and outside," Damarnin told RTL radio. "We need to understand that there have been and there will be other events such as these terrible attacks."
Thursday's attack, on the birthday of the Prophet Mohammad, took place at a time of growing Muslim anger across the globe at France's defence of the right to publish cartoons depicting the prophet. Protesters have denounced France in street rallies in several Muslim-majority countries.
Tens of thousands of Muslims protested in Bangladesh on Friday, chanting slogans such as "Boycott French products" and carrying banners calling French President Emmanuel Macron "the world's biggest terrorist" as they marched in the streets of the capital Dhaka.
Macron has deployed thousands of soldiers to protect important sites such as places of worship and schools, and the country's security alert is at its highest level.
SUSPECTED ATTACKER CAME FROM TUNISIA
France's chief anti-terrorism prosecutor said the man suspected of carrying out the Nice attack was a Tunisian born in 1999 who had arrived in Europe on Sept. 20 in Lampedusa, the Italian island off Tunisia that is a main landing point for migrants from Africa.
A Tunisian security source and a French police source named the suspect as Brahim Aouissaoui.
A judicial source said on Friday that a 47-year-old man had been taken into custody on Thursday evening on suspicion of having been in contact with the perpetrator of the attack.
The Nice attack occurred just under two weeks after Samuel Paty, a school teacher in a Paris suburb, was beheaded by an 18-year-old Chechen who was apparently incensed by the teacher showing a cartoon of the Prophet Mohammad in class.
Speaking outside the church in Nice on Thursday, Macron said France had been attacked "over our values, for our taste for freedom, for the ability on our soil to have freedom of belief...And I say it with great clarity again today: We will not give any ground."
Prosecutor Jean-Francois Ricard said the suspected attacker had entered the city by train early on Thursday morning and made his way to the church, where he stabbed and killed the 55-year-old sexton and beheaded a 60-year-old woman.
He also stabbed a 44-year-old woman, who fled to a nearby cafe where she raised the alarm before dying, Ricard said. Police then arrived and confronted the attacker, who was still shouting "Allahu Akbar", and shot and wounded him.
Tunisia said the man was not listed by police there as a suspected militant and authorities have begun their own investigation.
France, with Europe's largest Muslim community, has suffered a string of Islamist militant attacks in recent years, including bombings and shootings in 2015 in Paris that killed 130 people and a 2016 attack in Nice in which a militant drove a truck through a seafront crowd celebrating Bastille Day, killing 86.
(Reporting by Matthias Blamont; Editing by Angus MacSwan)
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