Gov. Dannel P. Malloy left the door open Monday for the legislature to offer amnesty to gun owners whose mailed-in registration paperwork for newly banned rifles and ammunition magazines arrived after the deadline.

Gun regulations passed last year in response to the Sandy Hook shootings banned ammunition magazines that carry more than 10 rounds and increased the number of rifles prohibited in Connecticut. The law gave people who had previously purchased them until the end of the year to register to keep them. Gun owners registered about 50,000 rifles and 38,000 magazines before the deadline.

But post offices closed early on Dec. 31 and some of the paperwork that was dropped in the mail that day was postmarked after the deadline. Michael Lawlor, Malloy’s criminal justice policy adviser, said Monday that the state received 226 assault weapon applications and 506 high-capacity magazine declarations postmarked after the deadline.

Asked Monday about a potential grace period for the late applications, Malloy said it is possible because the state has retained the late paperwork. But he said the legislature would need to change the law in order for them to be accepted.

“I understand that some people are saying that they went to the post office to mail in their registration. That’s why we’ve saved — in accordance with what I thought was the right thing to do — those forms. So if the legislature, in its wisdom, was to allow for that to happen, we’re in a position to know who actually sent in those forms,” Malloy said.

The issue came up during a press conference Monday because Senate Minority Leader John McKinney, R-Fairfield, wrote to Lawlor earlier this month and requested that the state accept and process the applications that were mailed in but postmarked late.

McKinney said Monday that he does not think it would take legislative action to allow the Malloy administration to accept the paperwork, just a more lenient interpretation of the law as its written. He said the Department of Emergency Services and Public Protection has chosen to accept paperwork postmarked by a certain date, when it could just as easily accept paperwork placed in the mail by that date.

“That was their choice to interpret it that way. They didn’t have to. They could have said anything dropped off on the 31st,” he said. “I think the odds that someone filled all the paperwork out and went down to the post office on Jan. 2, given the small numbers we’re talking about, are extremely rare.”

The governor insisted more than once that accepting the paperwork would require changing the law. He said the forms were saved “because we understood, but I don’t have the power to do that. That would require legislative action.”

Asked if he would be proposing that legislation, Malloy said, “based on who’s inquiring, I would assume that they’re going to do that,” presumably referring to McKinney.

Malloy has not announced whether he will seek re-election this year but is widely expected to run. McKinney, meanwhile, is one of several Republicans currently running for governor. Both supported the underlying gun control law that created the deadline.

The law is deeply unpopular with members of the state’s gun rights organizations, whose membership numbers have swelled in the past year. One Republican candidate, Tom Foley, has already appealed to the Connecticut Citizens Defense League for political support.

However, McKinney said he has not pushed for the registration amnesty with the hopes of scoring political points. He said the gun owners whose applications arrived late made a good faith effort to comply with the law and he never publicized his correspondence with Lawlor.

“I would never guess that [the gun owners] would switch their opinion of me based on this. But more importantly, I never told anybody about it,” he said.