NEW YORK >> A New York City police officer who suffered a serious head wound after being attacked by a hatchet-wielding man remains in critical but stable condition, police said Friday.

Police say another officer who was hit in the back of the head in the Thursday attack is in stable condition on Friday.

The attacker was shot and killed by police.

Security videotape and witness accounts appeared to leave no doubt that the man purposely targeted four rookie New York Police Department officers, police said. Moments before the attack, he was seen on a street corner crouching down to pull the hatchet out of backpack before he charged the officers and began swinging the hatchet with a two-handed grip, police said.

Asked if the attack could be related to terrorism, Police Commissioner William Bratton didn’t rule it out. He cited the fatal shooting of a soldier in Canada earlier this week — what officials there have called a terror attack — as reason for concern.

"This early on, we really cannot say yes or no to that question," Bratton said Thursday.

The attack occurred at about 2 p.m. while the officers were standing together on foot patrol, police said. Without a word, the man swung at an officer who blocked the blow with his arm. Another officer was hit in the back of the head and fell to the ground.

As the man raised the hatchet again, the two uninjured officers drew their weapons and fired several rounds, police said. The bullets killed the assailant and wounded a female bystander, police said.

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Associated Press writer Tom Hays contributed to this report.