This photo provided by the AP on the condition that its source not be revealed, shows Karim Cheurfi.
He also called for campaigning generally to be suspended, although from midnight on Friday the law says it has to stop anyway.
The attack comes three days ahead of the first round of the presidential election to choose two candidates for a run-off May 7.
Another witness identified only as Ines told France's BFM TV she heard a shooting, saw a man's body on the ground and the area was quickly evacuated.
Police swept through the family home in Chelles in eastern Paris looking for evidence of links with Daesh "ISIL", who claimed he was acting on their behalf.
He then tried to run along the pavement as he continued firing, injuring two further officers and a female tourist before authorities opened fire, killing the attacker.
The gunman pulled up next to the police vehicle, took out an automatic weapon and started shooting, New York Post quoted Interior Ministry Spokesman Pierre-Henry Brandet, Efe news reported.
The gunman wounded two police officers before being shot dead by security forces on the Champs Elysees.More news: Trump takes direct aim at Canadian dairy
A note expressing support for Isis has reportedly been found near the body of a gunman who shot a police officer dead in the centre of Paris.
Despite the gunman being killed, police are still on high alert and officers have been seen pointing their weapons at members of public as they clear the area.
In a statement from its Amaq news agency, the group gave a pseudonym for the shooter, Abu Yusuf al-Beljiki, indicating he was Belgian or had lived in Belgium.
Fillon called for a halt to campaigning after the shooting in Paris.
Steve White, chairman of the Police Federation of England and Wales, said: "Once again the police family is in mourning and it serves to underline how courageous officers are putting their life on the line day in and day out to protect the public". Subway stations were closed off.
The gunfire sent scores of tourists fleeing into side streets.
"For years now, I've been saying what needs to be done", she said.
"Some were crying. There were tens, maybe even hundreds of them".More news: Tillerson: Iran Deal Fails to Achieve Nuclear-Free Objective
President Francois Hollande has said he was convinced the atrocity was terror-related. A spate of nationwide Islamist attacks over the last two years has killed more than 230 people.
"Nothing must hamper this democratic moment, essential for our country", Prime Minister Bernard Cazeneuve said after a high-level meeting Friday that reviewed the government's already heightened security plans for the two-round presidential vote that begins Sunday.
Two Presidential hopefuls cancelled rallies scheduled for Friday.
The 63-year-old Fillon is one of four candidates who polls suggest is capable of qualifying for the runoff vote after voters cast their ballots in the first round on Sunday.
Australian prime minister Malcolm Turnbull offered his condolences to the killed policeman and urged Australians in Europe to be on their guard.
Malcolm Turnbull urged travellers to check for security warnings on the Australian Department of Foreign Affairs and Trade website.
"We shall be of the utmost vigilance, especially in relation to the election", he told the nation on television.
"I will say it once again [at later press conference], detail my battle plan to protect the French from this terrorist threat starting with taking back control of our national borders because terrorists come through our borders in all circumstances and with absolute peace of mind".More news: Can Far-right candidate Marine Le Pen win the French election?
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