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New York (CNN) -- A broad-daylight hatchet assault on a group of New York police officers -- leaving one critically injured with a head wound -- was carried out by a self-radicalized convert to Islam in what officials Friday termed a terrorist attack.

Officer Kenneth Healey, who remains in critical condition, and three of his on-duty colleagues were posing for a picture on the sidewalk Thursday afternoon when a hatchet-wielding man charged at them "unprovoked," according to Police Commissioner Bill Bratton.

The attacker, identified as Zale H. Thompson, was hiding behind a bus shelter as if he was waiting to attack the officers, according to a law enforcement official, who said it almost appeared as if he were stalking them.

"This was a terrorist act," Bratton said Friday.

NYPD officer injured by ax-wielding man

Was attacker an Islamic extremist?

Thompson converted to Islam two years ago and then at some point self-radicalized, John Miller, the NYPD's deputy counterterrorism chief, told reporters Friday. Miller said Thompson was self-directed in his actions, and he had no affiliations with any particular group.

Thompson was unemployed, and police said his parents described their son as a depressed recluse who spent much of his time online.

A common theme in his social media presence was "anti-Western, anti-government and in some cases anti-white," Miller said.

According to police, Thompson's recent Internet activity revealed he had searched for things such as beheadings, al Qaeda, ISIS and al Shabaab, indicating that "he had been thinking about (carrying out an attack) for some time," said Miller.

Healey, 28, was struck in the back of the head. New York Mayor Bill de Blasio said Friday Healey was in critical but stable condition. Officer Joseph Meeker, 24, was struck in the arm. He was treated and released, according to de Blasio.

The remaining two officers fired at the 32-year-old Thompson, killing him.

In the chaos, one of the officer's bullets struck a nearby pedestrian in her lower back. De Blasio said Friday that she was in critical but stable condition.

De Blasio praised the officers' swift response in the attack, which police said lasted seven seconds. "Here are four rookie cops, just starting out in their career, when the absolute unexpected happened," de Blasio said at a Thursday press conference. "They responded exactly as their training dictated and ended the situation -- thank God -- very, very quickly. "

In the aftermath, some observers questioned if the attack was tied to recent calls by radicals to strike the military and police, especially on the heels of separate attacks on officers in Canada earlier this week.

On Wednesday, a soldier was shot and killed as he stood guard at Canada's National War Memorial in Ottawa. Officials said the gunman had connections to jihadists who shared a radical Islamist ideology. Two days before, another Canadian soldier -- this one in Quebec -- was run over and killed by another man whom the Royal Canadian Mounted Police called "radicalized." Like the one in Queens, both attacks were carried out in public and in daylight.

CNN's Shimon Prokupecz reported from New York, Greg Botelho, Ray Sanchez, Jim Sciutto, Sonia Moghe and Leigh Remizowski contributed to this report.