The Common Sense Firearms Licensing Act would also make firearms-safety courses mandatory for first-time gun owners and prevent people convicted of spousal assault from legally owning guns.
The bill would also give gun owners who allow their weapon permits to lapse a six-month grace period to renew them.
While their permits are expired, firearms owners won't be allowed to buy new guns or ammunition, but would no longer face possible jail time as a result of the expiry.
The government also plans to combine two licences currently needed to own and use firearms the possession and acquisition licences.
Once the law is passed, there will be just one licence required.
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