Police arrested a 48-year-old white man suspected of carrying out the attack on the group of Muslims near Finsbury Park mosque shortly after midnight.
Security Minister Ben Wallace said the man was "not known to the authorities in the space of extremism or far-right extremism".
In addition to the man who died, 11 people were injured, with nine taken to hospital, two in a very serious condition, police said.
"This vicious terrorist attack against innocent worshipers is clearly aimed at compromising the values of peace, tolerance and diversity", Algerian Foreign Ministry's spokesman Abdelaziz Benali Cherif said in a statement.
After being seized, he said he had wanted to kill "many Muslim people", one witness told journalists.
"These were the kinds of comments people were yelling out", she said.
Neil Basu, senior national co-ordinator for counter-terrorism policing, said restraint shown by locals was "commendable".
The terror probe led investigators to the Welsh capital Cardiff, where they searched a property said by media to be the home of Darren Osborne.
Speaking to reporters Monday, the imam, Mohammed Mahmoud, said he and others acted to "extinguish any flames of anger or mob rule that would have taken charge had this group of mature brothers not stepped in".
Earlier this month on London Bridge, Islamic extremists used a vehicle and then knives to kill eight people and wound many others on the bridge and in the popular nearby Borough Market area.
Opened in 1994, Finsbury Park Mosque is an unassuming five-story redbrick building in residential north London, close to Arsenal Football Club's Emirates Stadium.
Manchester was also hit on May 22 when a suicide bomber killed 22 people at an Ariana Grande concert.
The London Ambulance Service said it was responding to the incident.
Northumbria Police say there will be additional patrols taking place around all places of worship, including mosques this week.
The Finsbury Park Mosque was once a notorious hub for radical Islamists but has changed markedly in recent years under new management.
A witness told CNN's Phil Black the van "came to a stop, and that's when they were able to apprehend the driver. they were able to pull him out".
The mosque itself gained notoriety more than a decade ago for sermons by radical cleric Abu Hamza al-Masri, who was sentenced to life in a US prison in January 2015 after being convicted of terrorism-related charges. Attendance has greatly increased since then among worshippers from various communities, according to the mosque's website.