Castaner said it "is very hard to anticipate" attacks when they were staged by people who were not on the police radar.
In the video obtained by ABC News, the attacker lunges at a policeman with a hammer.
A second officer shot and wounded Ikken after the initial blow. The officer was wounded and the assailant was hospitalized, police said.
It is said that hundreds of people were at the cathedral when the incident occurred.
A hammer and kitchen knives were found on the assailant, as well as a student identity card indicating he was from Algeria, Collomb said.
The injured officer is recovering in the hospital, according to police.
Paris prosecutors have opened a counter-terrorism investigation into the latest incident.
Authorities in Paris asked the public to stay away from Notre-Dame, one of France's biggest tourist attractions situated on the banks of the Seine river in the heart of the capital. France is still in a state of emergency after the November 2015 Paris attacks that killed 130 people.
Kyle Riches, a tourist from San Francisco, was with his wife walking through the plaza outside Notre-Dame when they heard gunshots and dropped to the ground.
"People were extraordinarily calm, helping those who don't speak English translate", she said, adding that she felt safe but the situation was terrifying.
Over 1,000 people were inside the cathedral at the time of the attack.
Gerard Collomb, the French interior minister, told reporters that the attack occurred around 4:20 p.m. when the man approached three police officers from behind and started hitting one of them with a hammer. He also confirmed that the condition of the police officer was not serious.
Tourists who took refuge in the cathedral were being checked by police before being allowed to leave.
He said he and his wife saw police holding their guns up as they ran toward someone. The attacker's motives were unknown.
The police department tweeted about the operation on Tuesday afternoon.
Police sources said the officer sustained only minor injuries in the assault, which comes with France on high alert for jihadist strikes after a weekend attack in London.