Mohammed Yassar Yaqub, 28, died after police opened fire on the car he was travelling in during a “pre-planned” operation near the M62.
The police watchdog said a “non-police issue” firearm was later found in the car and it was “working hard” to establish the circumstances around the fatal swoop.
Around 100 mourners gathered at the spot near Huddersfield, West Yorkshire, on Wednesday night to hold a vigil where Mr Yaqub’s family and friends laid flowers.
Speaking at the roadside Mohammed Yaqub said he felt his son was “killed unlawfully”.
“He hasn’t got a bad past, because he’s never been convicted of anything,” he told the BBC.
The operation on Monday evening saw a number of vehicles stopped at two locations, one in Bradford and a second at Ainley Top, just north of Huddersfield.
The car Mr Yaqub was travelling in was intercepted at Junction 24 of the M62 at around 6pm. He died at the scene.
West Yorkshire Police said five men - three in Huddersfield and two in Bradford - were arrested on suspicion of possessing a firearm with intent to cause fear. Two men, aged 26 and 30, have since been bailed.
The Independent Police Complaints Commission (IPCC) said it had taken “initial accounts” from the police officers involved and it was seeking relevant CCTV footage.
A post-mortem examination of Mr Yaqub’s body was due to take place on Wednesday.
Mr Yaqub senior said he wanted “answers, full answers, nothing but the truth” about his son’s death.
“How can you kill someone like this, at a time like this, without giving him a chance to get out or anything? We’re not in America, we’re not in third-world countries,” he said.
Wednesday evening’s vigil carried off “peacefully and respectfully”, according to the BBC.
According to the creators of a Facebook page called Justice 4 Mohammed Yasser Yaqub he was killed unlawfully.
Nearly 2,000 people have followed the page that states: “Mohammed Yasser Yaqub murdered by Yorkshire Police! Ambushed, assassinated and left to die.. How can we live in a world that thinks this is acceptable?”
A demonstration against the police killing in Bradford on Tuesday night saw traffic brought to a standstill in parts of the city centre and several vehicles, police and civilian, were damaged, West Yorkshire Police said.
Officers were deployed in the city centre after protesters carrying banners reading “police don’t murder” blocked roads at around 7.15pm.
A small number of the demonstrators were involved in disorder that caused damage to several vehicles, police said.
West Yorkshire Police said it empathised with the “heightened tensions” and was working to maintain community cohesion, while Naz Shah, Labour MP for Bradford West, appealed for calm.
Mr Yaqub was from Crosland Moor, Huddersfield. In 2010, he was cleared of attempted murder and a firearms offence after it was alleged that he opened fire on a car in Birkby Hall Road, Huddersfield.
People living close to Rudding Street said on Tuesday that Mr Yaqub’s house was targeted by gunmen more than a year ago.
In June 2015, police said two people suffered minor injuries when a shotgun was fired in Rudding Street by gunmen in a “targeted attack” as children played.