Canada's prime minister has said he will speed up plans to bolster laws on "surveillance and arrest" after a deadly attack on parliament in Ottawa he said was designed to instill fear and panic.

Parliament reopened on Thursday, a day after a gunman, identified as Michael Zehaf-Bibeau, was shot dead after storming into its main building shortly after killing Nathan Cirillo, a soldier guarding the nearby national war memorial.

Parliament opened with applause for the sergeant who shot Zehaf-Bibeau, and a moment's silence for the dead soldier.

Harper's opened his speech to MPs by stating: "I know we will always stand together."

"The objective of these attacks was to instill fear and panic in our country. Canadians will not be intimidated. We will be vigilant, but we will not run scared. We will be prudent but we will not panic."

Harper pledged to speed up a plan already under way to bolster police powers in the areas of "surveillance, detention and arrest".

Canadian police on Thursday said Zehaf-Bibeau was working alone, contrary to statements on Wednesday that officers were looking for "one or more people" even after the gunman was shot dead. Police offered no motive for the attack.

Mother 'crying for victims'

The mother of the attacker meanwhile said she was crying for the victims of the shooting, not her son.

We also wish to apologise for all the pain, fright and chaos he created. We have no explanation to offer.

Susan Bibeau, mother of the attacker

"Can you ever explain something like this?'' Susan Bibeau said in an interview with the Associated Press. "We are sorry.''

"If I'm crying it's for the people. Not for my son."

"I am mad at my son," she said in a separate email to the agency. "I, his mother, spoke with him last week over lunch, I had not seen him for over five years before that,'' the email said. "So I have very little insight to offer."

She said that no words could express the sadness she and her husband were feeling over the death of the soldier

"We are so sad that a man lost his life. He ... leaves behind a family that must feel nothing but pain and sorrow. We send our deepest condolences to them although words seem pretty useless. We are both crying for them."

"We also wish to apologise for all the pain, fright and chaos he [Zehaf-Bibeau] created. We have no explanation to offer."

The Ottawa attack came two days after another man, who Harper described as an "ISIL-inspired terrorist" ran over two soldiers in a parking lot in Quebec, killing one and injuring another before being shot to death by police. 

Source: Al Jazeera and agencies