One officer was killed and two police officers were seriously wounded when the attacker emerged from a auto and used an automatic weapon to shoot at officers outside a Marks & Spencer's department store at the centre of the Champs-Elysees, anti-terrorism prosecutor Francois Molins said.
The officials - who spoke on the condition of anonymity - said the gunman was detained at the end of the month after speaking threateningly about the police, but later released due to a lack of evidence.
The attack came three days before the first round of balloting in France's tense presidential election.
Bystanders are frisked by police officers near the Champs Elysees avenue in Paris, France, after a fatal shooting in which a police officer was killed along with an attacker.
Mr Molins, who handles terrorism investigations nationwide, said authorities had identified the killer, but he declined to provide the gunman's identity because police raids and the search for potential accomplices were still underway.
U.S. president Donald Trump, speaking at a press conference in Washington, said the incident "looks like another terrorist attack" and sent his condolences to France.
Conservative candidate Francois Fillon and Marine Le Pen, leader of the far-right National Front, both talked up their tough law-and-order stances while centrist front-runner Emmanuel Macron stressed he was also up to the challenge.
A statement from the Islamic State group published by its propaganda agency Amaq said the attacker was "one of the Islamic State's fighters". He was taken into custody but while being questioned grabbed another officer's gun and shot him three times, the source said. The attacker, a 29-year-old Egyptian, was seriously injured.
French media reported Cheurfi was on the radar of intelligence services.
"We have a great determination to battle terrorism here and everywhere our forces are engaged", the head of state said in a televised address.More news: Australia scraps visa for skilled foreign workers
He fled on foot before the driver of the other auto and the passenger - a trainee police officer - caught up with him.
Macron said he canceled campaign stops out of a sense of "decency" and to allow police to concentrate resources on the investigation.
German Chancellor Angela Merkel expressed her condolences to Hollande and said her sympathy "goes out to the victims and their families", according to her spokesman Steffen Seibert.
"She won't be able to protect our citizens", Macron said.
Police in Paris are investigating a shooting, which ISIS has claimed responsibility for, that targeted two police officers near one of the city's popular landmarks.
Police shot and killed the gunman after he opened fire on a police van on Paris' most famous boulevard on Thursday night.
A spokesman for the interior ministry paid tribute to the fast reflexes of police at the scene who managed to kill the gunman and prevent further bloodshed on a busy spring-time evening.
French investigators searched a home early Friday near Paris believed linked to Thursday's attack.
The attack appeared to fit a pattern of European extremists targeting security forces and symbols of state to discredit, take vengeance on or destabilize society.
- February 3: A man armed with a machete in each hand attacks four soldiers on patrol at Paris's Louvre Museum, shouting "Allah Akbar".