The shooter, whose identity is still unknown, has reportedly been shot dead.
The officials had no other details about the attacker.
"We don't have a precise idea of the origin of the shots fired", he said.
French President Francois Hollande said he believes the incident is likely a terrorist attack.
Centrist candidate Emmanuel Macron offered his thoughts to the family of the dead officer and Socialist Benoit Hamon tweeted his "full support" to police against terrorism.
Three police sources said, however, that the shooting could have been an attempt at an armed robbery. A police source also said there had been two assailants, and a witness told Reuters that one man got out of a auto at the scene and began shooting with a machine gun.
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Paris police spokeswoman Johanna Primevert says unidentified gunman appeared to be alone when he allegedly opened fire on a police vehicle.
The claim of responsibility came unusually swiftly for the group, which has been losing territory in Iraq and Syria.
"They were running, running", said 55-year-old Badi Ftaïti, who lives in the area. "There were tens, maybe even hundreds of them".
"It looks like another terrorist attack", Trump said. "It just never ends".
"We had to hide our customers in the basement", Choukri Chouanine, manager of a restaurant near the site of the shooting, told AFP, saying there was "lots of gunfire".
The attack came three days before the first round of balloting in France's presidential election.
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Emergency vehicles blocked the wide avenue that cuts across central Paris between the Arc de Triomphe and the Tuileries Gardens, normally packed with cars and tourists.
Police authorities called on the public to avoid the area.
There are conflicting reports about how many people were involved in the attack, however a police spokesman said there were two people, while other reports suggested the gunman was armed with a Kalashnikov.
The attacker opened fire on a police van with an automatic weapon before being killed.
One officer was killed and another was wounded.
Brandet says the police officers were "deliberately" targeted. He said it is too early to know if the gunman had an accomplice. Security is high preceding the vote after police said they arrested two men Tuesday in what they described as a thwarted terror attack.
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Another witness identified only as Ines told French television station BFM that she heard a shooting, saw a man's body on the ground and the area was quickly evacuated by police. The shooting started during the last TV show with all 11 presidential candidates before the first round of the election on Sunday.