OTTAWA -- The fatal shooting of a soldier at the National War Memorial and the subsequent gunfire on Parliament Hill on Wednesday have renewed concerns about security in the capital.

The shootout left a suspect dead in the Centre Block, sent MPs fleeing and forced the lockdown of much of the downtown core.

MPs and senators have been nervous for years about how easily members of the public can access the Parliament Buildings. Canada's role in the campaign against ISIL has heightened concerns in recent weeks.

"I think the intention was to try to make Parliament not look like Fort Knox," Liberal MP Marc Garneau said. "But we've crossed a river today."

Garneau pointed out that while visitors go through metal detectors, most parliamentary offices are easily accessible once those people are in the buildings.

"The point is, somebody who decides that they want to rush the building can walk up, rush in, show their weapon and then rush into the building before anybody can really effectively do anything," he said.

Karl Belanger, principal secretary to NDP Leader Tom Mulcair, said there's no question procedures will need to be reviewed and fixed so that such a breach never happens again.

NDP MP Charlie Angus said that as gunfire echoed through the Hall of Honour during the party's caucus meeting on Wednesday morning, "suddenly those parliamentary caucus doors looked very, very flimsy."

But Angus added he hopes the Hill doesn't become fortress as a result of the shooting.

"I just think what's really important to remember from this is that Parliament Hill is an incredible public place that's open for people to play football and come and protest and sit and have their lunches, do their yoga," he said.

"We can't lose that. We need to make it more secure, we need to make sure people can be safe ... but we can never lose sight (that it's) an open place where Canadians feel welcome."

Liberal MP John McKay had the same feeling.

"That building is the people's building and we've been able to pride ourselves on its accessibility to people," he said. "I hate to think of us shutting it down because of both paranoia and legitimate fears. It really changes everything."

Earlier, some MPs asked for a Commons committee hearing into momentary delays inflicted upon parliamentarians last month as they tried to get to the House of Commons and were held up by the German president's motorcade.

MPs say their ability to move freely is a question of parliamentary privilege, ranking with their right to call for witnesses and documents and to say what they want in the Commons.

The hearing was held Tuesday, the day before the shootings.

- With files from Joan Bryden in Ottawa.