* Suspect arrested late on Thursday

* French interior minister says more attacks likely

PARIS, Oct 30 (Reuters) - France is engaged in a war against Islamist ideology and more militant attacks on French soil are likely, the interior minister on Friday.

Gerald Damarnin was speaking a day after a knife-wielding attacker shouting "Allahu Akbar" (God is Greatest) beheaded a woman and killed two other people in a church in Nice before being shot by police and taken away.

"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."

A judicial source said 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.

Chief anti-terrorism prosecutor Jean-Francois Ricard said the man suspected of carrying out the 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 suspected attacker as Brahim Aouissaoui. Ricard said the suspected attacker had entered the city by train early on Thursday morning.

The suspect was in hospital in critical condition, he said.

The Nice attack occurred just under two weeks after a school teacher in a Paris suburb was beheaded by an 18-year-old attacker who was apparently incensed by the teacher showing a cartoon of the Prophet Mohammad in class.

(Additional reporting by Sudip Kar-Gupta, Matthias Blamont; editing by Angus MacSwan)