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(CNN) -- The Ottawa gunman had "connections" to jihadists in Canada who shared a radical Islamist ideology, including at least one who went overseas to fight in Syria, multiple U.S. sources told CNN on Thursday.

However, Canadian Foreign Minister John Baird told CNN's Christiane Amanpour that there is "no evidence at this stage" that Michael Zehaf-Bibeau was linked to a wider group, or network, of jihadists.

"There's no evidence at this stage for us to know that. Obviously there's an investigation going on, and we hope to learn more in the ... coming days. It was clear that, police authorities now have announced, that he was acting alone yesterday," he said.

According to two U.S. counterterrorism officials, Zehaf-Bibeau was connected to Hasibullah Yusufzai through social media. Yusufzai is wanted by Canadian authorities for traveling overseas to fight alongside Islamist fighters in Syria, The Globe and Mail, a Canadian newspaper, reported.

The sources said the two communicated via social media and the Internet, but it does not appear they were close.

Early indications are that Zehaf-Bibeau's connections to other extremists were "interactions" online, including extremist sites, a different U.S. source said.

The activity was "attenuated," or limited, the source said, noting it appears, so far, that Zehaf-Bibeau had a low profile.

There is no evidence so far that he had any "operational links" to other jihadists, according to the source, who drew a distinction between interacting online and plotting an attack.

American officials are reportedly scouring databases and communications for possible links to American-based jihadists.

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Other radicalized people connected to Zehaf-Bibeau are still believed to be living in Canada, U.S. law enforcement officials said.

"The investigation is ongoing and will rapidly determine if Zehaf-Bibeau received any support in the planning of his attack," Royal Canadian Mounted Police Commissioner Bob Paulson told reporters Thursday.

Officials now have "information that suggests an association with some individuals who may have shared his radical views," he said. Paulson didn't say who these people are or how Zehaf-Bibeau may have interacted with them.

The gunman

Authorities are still in the early stages of their investigation, but they are beginning to piece together the puzzle.

They released surveillance video Thursday that shows events on Wednesday. In the footage, a vehicle pulls up near Parliament, and a man exits, running with a large gun as people run from him. In other footage, this same man then gets into another vehicle, drives to a nearby building, gets out and runs armed into the building pursued by law enforcement.

Baird, in a Thursday night interview with Anderson Cooper on CNN, described the chaos inside the building, saying Zehaf-Bibeau "ran right by the room where the entire government caucus was. We could hear the ringing out of rifle fire and then the huge amount of semiautomatic noise.

"We didn't know if the door would be banged open and that we'd all be sprayed," he said.

Baird said the sergeant-at-arms of the House of Commons shot and killed Zehaf-Bibeau at the door to the library, which contained a tourist group as well as employees.

"You could have seen more than a dozen killed if he (the sergeant-at-arms) hadn't taken such quick action," Baird said.

Zehaf-Bibeau was a Canadian citizen who may have had dual Libyan-Canadian citizenship, said Paulson. The police commissioner said Zehaf-Bibeau was born in Montreal and lived in Calgary and most recently Vancouver.

Zehaf-Bibeau had been in the Canadian capital since at least October 2 "to deal with a passport issue and ... he was also hoping to leave for Syria," Paulson said. Paulson also said of Zehaf-Bibeau: "According to some accounts, he was an individual who may have held extremist beliefs."

Zehaf-Bibeau was applying for a passport -- an application that was under investigation -- at the time of the attack, but had not had his passport revoked, as has been previously reported, Paulson said.

"I think the passport figured prominently in his motives," said the police commissioner. "However, we have not come to ground completely on his motivations for this attack. But clearly, it's linked to his radicalization. Clearly, it's linked to his difficult circumstances."

According to Paulson, investigators thus far have not found any connection between Zehaf-Bibeau and Martin Rouleau Couture -- who authorities say ran down and killed a Canadian soldier in Quebec on Monday. Police later killed Couture.

Who was Ottawa shooter Michael Zehaf-Bibeau?

Zehaf-Bibeau was born as Michael Joseph Hall in 1982. He had criminal records indicating infractions related to drugs and violence and other criminal activities, Paulson said.

In a pre-trial psychiatric evaluation performed in 2011, a doctor noted Zehaf-Bibeau at that time had been "a devoted Muslim for seven years."

The gunman's mother, Susan Bibeau, spoke to The Associated Press by phone. She struggled to hold back tears and said she didn't know what to say to those hurt in the attack.

"If I'm crying, it's for the people," Bibeau reportedly said. "Not for my son."

"I'm mad at my son," she said in a separate email to the AP.

Harper: "We will not run scared'

Canadian lawmakers returned to work Thursday, giving a standing ovation to the ceremonial Parliament official credited with taking down the gunman who killed a soldier and shook the Parliament area.

"We'll be vigilant, but we will not run scared. We will be prudent, but we will not panic. And as for the business of government, well, here we are -- in our seats, in our chamber, in the very heart of our democracy," Canadian Prime Minister Stephen Harper told the House of Commons in Ottawa.

Lawmakers stood and cheered Sergeant-at-Arms Kevin Vickers, who officials say took down the suspect in the halls of Parliament minutes after the killing of Canadian army reservist Cpl. Nathan Cirillo at a war memorial nearby.

Vickers, who regularly leads a procession into the House as sessions begin, stood with his ceremonial mace and appeared to be emotional during the ovation. He later released a statement saying he is touched by the attention.

"However, I have the support of a remarkable security team that is committed to ensuring the safety of Members, employees and visitors to the Hill," Vickers said.

It was a step toward normalcy for a government district that was widely locked down for hours after the shootings at Canada's National War Memorial and Parliament Hill.

Authorities say Zehaf-Bibeau shot and killed Cirillo, who was standing guard at the war memorial on Wednesday morning. The gunman then entered the nearby main Parliament building in downtown Ottawa, where witnesses say shots were fired -- many by security officers -- before he was shot dead.

A plainclothes constable who was working security at Parliament was shot in the leg, according to a House of Commons official briefed on the investigation. The injury is not life-threatening, and the constable was treated at a hospital and released, the official said on condition of anonymity.

The shootings left government workers and others locked inside offices for a large portion of the day while police searched buildings to ensure that no other culprit was loose.

Wednesday's deadly attack was the second on Canadian soldiers this week. On Monday, Couture, a convert to Islam who Canadian authorities said was "radicalized" hit two soldiers with a car in Quebec, killing one of them, before he was killed.

Lawmakers pay respects to soldier

There was an incident Thursday morning as the Prime Minister and his wife were laying a wreath, in memory of Cirillo.

An eyewitness said a man began yelling.

He reached into his jacket, then pulled out a white scarf, and wrapped it around his face. About a dozen police ran towards him, the eyewitness said.

The Prime Minister and his wife had intended to stay longer, but his security team surrounded them and quickly ushered them out.

"He's lucky he wasn't shot," the eyewitness said of the man. The man was apprehended at the scene.

Jim Cirillo, Nathan Cirillo's uncle, told CBC News that Cirillo's father is in Costa Rica and might not yet know about his son's death.

"I don't know if life is fair," Jim Cirillo, said his voice breaking with emotion. "He didn't deserve that. I don't know how someone could have picked him out and just did that."

Before Parliament reopened, lawmakers gathered outside the memorial -- some holding flowers -- for a moment of silence for Cirillo.

"This was very off the cuff," lawmaker Charlie Angus told CNN on Thursday morning. "I think parliamentarians really just felt that before we walked into the Parliament buildings, we had to pay respect to a young man who gave his life for his country."

Angus said the soldiers' killings this week left the government with plenty of questions.

"The questions we need to ask ourselves (include), 'How are these people getting this crazy ideology that's inspiring them to do these copycat killings?' " he said.

Another question, he said: What can society do to deal with people who find themselves on the fringes? Issues of mental health, he said, need to be addressed.

"We cannot let people like this fall through the cracks and end up doing deranged killings," Angus said.

CNN's Ashley Fantz, Josh Levs, Catherine E. Shoichet, John Newsome, Pamela Brown, Greg Botelho, Elise Labott, Jim Sciutto, Pam Brown, Andrea Lewis, Ana Cabrera and Deb Feyerick contributed to this report.