Police have not publicly named the attacker, but ISIS said in a statement that his name is Abu Yousef Al-Baljiki, "The Belgian", and called him "one of the Islamic State fighters".
Spokesperson of the French interior ministry Pierre-Henry Brandet told local broadcaster BFMTV that the police officers were "deliberately targeted".
French authorities had not identify the gunman, but President Francois Hollande said there was "no doubt" the attack was terrorism.
So close to the presidential election, "the country's on edge", Eleanor says, adding that thousands of police officers are on the streets.
"The investigation has been entrusted to the Anti-Terrorist Section (SAT) of the Criminal Brigade and the Directorate General of Internal Security (DGSI)", Paris chief prosecutor's office said in a statement.More news: New details on federal investigation into Fox News
BFMTV also reported that another police officer was seriously injured and an unidentified man was hit by the "cross-fire" in the the Champs-Elysees area.
Candidates in the election said they had been warned about the Marseille attackers.
As the terror attack unfolded, police blocked off key roadways in the heart of the French capital and told people to avoid the area.
Many police vehicles can be seen on the avenue that passes numerous city's most iconic landmarks.More news: Opko Health Inc (NYSE:OPK) reported Beta of 1.72
Concerns over security have been raised since Tuesday when two men were arrested for plotting an attack before the French presidential election, which is set to begin on Sunday.
Marine Le Pen of the far-right Front National, Francois Fillon of the centre-right Republicains and centrist Emmanuel Macron have cancelled events scheduled for today, the last day of the campaign. I heard six shots, I was afraid.
He fled on foot before the driver of the other auto and the passenger - a trainee police officer - caught up with him.
One police officer and an attacker have been killed in a shooting in Paris on Thursday, according to CNN affiliate BFMTV and the French Interior Ministry. "We have to be strong and we have to be vigilant, and I have been saying it for a long time".More news: Love or hate 'em, Apple's Live Photos are coming to the web
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