Patrick has filed legislation that would, among other measures, restrict gun owners to purchasing one firearm a month; tighten access to high-powered rounds of ammunition; create four new types of firearms-related crimes; and mandate buyers to undergo background checks before purchasing weapons at gun shows.
The bill would also require Massachusetts courts to send all relevant mental health records to the state's criminal justice information system so the federal government could include this information in a national gun license registry.
House Speaker Robert DeLeo recently formed an eight-member panel to study the state's gun laws and make recommendations to the Legislature.
Wallace said the need for such a panel only demonstrates the complexity of the current rules.
"We need to reform the gun laws to make them understandable by citizens, law enforcement and prosecutors, because right now they are so convoluted there is no one in the state that has those answers," he said.
Wallace said he would consider backing Patrick's call for sharing mental health information with the federal government if the bill was rewritten to include only those people who had been determined by the courts to be a danger to themselves or others. As currently written, he said people who had been confined overnight for something as simple as a bad reaction to medication could be denied the opportunity to own a firearm.
Democrats Markey and Lynch alluded to Wednesday's gun owners rally in their joint statement and criticized the three Republicans who are seeking the U.S. Senate seat formerly held by Secretary of State John Kerry.
"While we may be competitors in the Democratic primary, we can both agree that it is deeply troubling to see our three Republican rivals siding more with the NRA and their activists who are descending upon Boston Common today, rather than with the President of the United States on the critically important issue of gun safety," the congressmen said.