The family of the man being held after London mosque attack say he has been "troubled for a long time".
Darren Osborne, 47, was arrested after pedestrians were targeted by a man driving a van near Finsbury Park Mosque in north London early on Monday.
Neighbours of the father-of-four from Cardiff said they were "shocked" when they saw pictures of him being arrested but one revealed he had called her Muslim children "inbred".
In a statement, Osborne's family said he had been "troubled for a long time".
"We are massively shocked. It's unbelievable. It still hasn't really sunk in.
"We are devastated for the families. Our hearts go out to the people who have been injured."
They said the 47-year-old was "not a racist" and had never expressed racist views, adding: "It's madness. It is obviously sheer madness."
The attack unfolded as a man who had been taken ill was receiving first aid from the public near the mosque, where people had been saying Ramadan night prayers. The van was driven at people who were helping him.
The man was pronounced dead at the scene and paramedics took nine people to three London hospitals while two others were treated for minor injuries.
Witnesses described hearing the driver, who was detained by members of the public before police arrived, shout: "I am going to kill Muslims."
Osborne was arrested on suspicion of attempted murder but Scotland Yard said he was later arrested for the commission, preparation or instigation of terrorism, including murder and attempted murder.
Images of the van showed it was rented from Pontyclun Van Hire, near Cardiff.
One of Osborne's neighbours, Edward Gardiner, 28, a self-employed builder and plumber, called police at 12.27am on Sunday morning to report concerns for the welfare of a man sitting in a Pontyclun Van Hire vehicle.
The man, who smelt of drink, was sleeping across the front three seats of the van with the door open, close to Osborne's home.
"I called police because I saw a random van in my cul-de-sac with someone drunk in it and the door open," Gardiner, who lives in a nearby property, said.
"I could smell alcohol on him and he was grunting and groaning. I poked him but he didn't respond so I called 101.
"I didn't think anything about it but then I saw the news reports and it was the same guy, the same van."