Wounded worshippers and family members of those killed in the Quebec City mosque shooting are calling on Prime Minister Justin Trudeau to outlaw assault weapons.

In a Monday letter to Trudeau, more than 75 people express dismay that the Liberal government's firearms bill does not ban assault rifles like the one carried by mosque shooter Alexandre Bissonnette.

Bissonnette, 28, pleaded guilty in March to six charges of first-degree murder and six of attempted murder.

Sentencing arguments in the case begin June 18.

Bissonnette began his January 2017 rampage with a .223-calibre Small Arms VZ58 Sporter rifle, which is legal, along with two illegal 30-cartridge magazines.

When the rifle jammed on the first shot, he turned to a handgun and five 10-bullet magazines.

The letter asks how much worse the carnage could have been had Bissonnette's rifle been working.

"What kind of society allows a single individual to have so much destructive, lethal power at their disposal?" the letter says.

Witnesses and survivors of the attack hope the pain of reliving details through recent media reports will be made worthwhile by a government effort "to make sure such mass shootings never happen again, first and foremost by removing legal access to assault weapons and their deadly accessories," the letter adds.

The federal bill introduced in March has been criticized by other gun-control advocates as too weak, while some firearms owners have called the legislation a misguided attempt to revive the ill-fated long-gun registry.

The bill would expand the scope of background checks on those who want to acquire a gun. Instead of just the five years immediately preceding a licence application, personal history questions would cover a person's entire lifetime.

The government says this measure will help keep guns out of the wrong hands.

Under the legislation, retailers would be required to keep records of firearms inventory and sales, a measure intended to assist police in investigating gun trafficking and other crimes.

The bill would also require purchasers to present a firearms licence, while the seller would have to ensure its validity.

The letter suggests the absence of explicit new curbs on access to assault weapons could be a result of the government bowing to firearms advocates.

"Please correct our serious misgivings regarding partisan matters that seem to be blocking consecutive governments from seriously addressing the gun issue. Yet this is a question of life and death."

Last November, some of the letter's signatories expressed concern to the government about far-right militias in Canada, including several in Quebec, that consider themselves to be foes of Muslims and other minorities.

The letter says Mark Holland, parliamentary secretary to Public Safety Minister Ralph Goodale, tried to reassure them by touting the government's anti-radicalization efforts.

"We had to respectfully interrupt Mr. Holland and explain that despite our obvious and enthusiastic support for the fight against radicalization, the most urgent priority should be to limit the destructive power in the hands of these militias as well as other ordinary civilians."

Scott Bardsley, a spokesman for Goodale, recently said the government looks forward to hearing feedback on its legislation during House of Commons public safety committee hearings and that it is "open to constructive proposals to strengthen the bill."

Goodale is slated to appear before the committee Tuesday.