They had no other details about him. A police source also said more shots had been fired at another location near the scene.
The Paris prosecutor's office said counterterrorism investigators are involved in the probe of Thursday's attack.
Tweeting following the attack, he said his thoughts are with the dead policeman's family and relatives of the wounded officers - adding that a national day of mourning will now be held.
BFMTV reported that the killer was known to security administrations and had talked about killing police officers on message boards.
The Islamic State claims responsibility for the attack, its news agency Amaq said.
The gunfire sent scores of tourists fleeing into side streets.More news: Pakistan SC orders further probe against Nawaz Sharif in graft case
The gunman is believed to have deliberately targeted the officers and was known to security services.
But the 55-year-old says visitors to the French "were running, running.Some were crying. There were tens, maybe even hundreds of them".
He says: "Paris is Paris".
"The indications that we have right now suggest a terrorist link", President Francois Hollande said in a televised statement after meeting his justice and interior ministers.
An officer has been killed and another hurt in a shooting on the Champs Elysées in Paris Thursday night, according to French media.
It was unclear how Trump concluded that terrorism may have been a factor.More news: Barcelona out of the UEFA Champions League
Emmanuel Macron, the centrist candidate that polls show has the best chance of being France's next president, said on France2 television that "the first duty of a president is to protect; this imponderable threat will be with us in coming years".
The attack came three days before the first round of balloting in France's presidential election.
Most of the Champs Elysees, just blocks away from the presidential palace, was closed off, three metro stations were shut, and police were telling people to avoid the area.
Emergency vehicles blocked the wide avenue lined with shops that cuts across central Paris between the Arc de Triomphe and the Tuileries Gardens, normally packed with cars and tourists. Two police officials, speaking on condition of anonymity because they weren't authorized to publicly discuss the investigation, said the attacker had been flagged as an extremist.
UPDATE (3:53 p.m. ET): One attacker shot a police officer as he sat in his cruiser at a red light, Fox News is reporting.More news: Google Home's assistant can now recognize different voices
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