OTTAWA — Prime Minister Justin Trudeau’s government proposed legislation on Tuesday to restore record-keeping requirements for some rifle and shotgun sales in Canada and to expand background checks for all gun owners in the country.

“Hard evidence shows a gun violence issue that is serious,” Ralph Goodale, the public safety minister, told reporters outside the House of Commons, citing increases in several categories of gun-related crimes, including a two-thirds rise in gun-related homicides.

Several members of the government, including Mr. Trudeau on social media, pointed out that the legislation did not bring back the much-debated national registry of rifles and shotguns, which was eliminated by the previous Conservative government six years ago.

Their assurances did little to assuage the concerns of some gun owners who objected to the new record-keeping.