Updated at 3:27 p.m. Feb. 19 to clarify the gun-and-ammunition sales policy at the NRA meeting.

Dallas Mayor Pro Tem Dwaine Caraway on Monday urged the National Rifle Association to find a new home for its annual meeting in May.

Caraway said that the NRA event, scheduled for May 3-6 at the Kay Bailey Hutchison Convention Center, is inappropriate for Dallas after the school shooting in Parkland, Fla., last week. The NRA's meeting will include firearms displays and exhibits, and the group's national elected officials will participate in leadership meetings. According to the website, ammunition sales are permitted, but on-site firearm sales are not.

In a written statement, Caraway said that it's "time to put the heat on the NRA." He followed up his written comments with a news conference outside City Hall in which he decried high-powered civilian-owned weapons and gun violence in Dallas, referencing both the 1963 Kennedy assassination and the July 7, 2016, ambush on police.

Caraway said asking the NRA to reconsider was "a tough call" but would put the city's residents first. He said the NRA's political positions would lead to demonstrations that Dallas would be forced to handle and that the organization needs to "come to the table" and be part of a solution.

"I would hope they would be sensitively moral themselves at some point," he said of the powerful interest group that has not bowed to past criticisms. "I would hope that the NRA would be watching, as I'm sure they are, around the country what has just taken place. They have children. They have families. At some point, they need to understand, and I think they do, that there will be opposition when they come here."

NRA media representatives did not immediately respond to messages for comment Monday morning.

Caraway largely sidestepped questions about what the city of Dallas could actually do about a legal event that already has a contract with the convention center. Instead, he said, other council members should take positions and that the city's attorneys could look into it.

It appears unlikely to go far. The city's ban of the Exxxotica event, which is still in its own legal fight, was based on its sexually oriented business ordinance. The NRA's meeting would appear more difficult to challenge.

Travis County commissioners in 2013 considered banning gun shows at the county's expo center, but ultimately voted such a measure down. Then-Attorney Gen. Greg Abbott warned of "a double-barreled lawsuit" if the county moved ahead with the ban.

And Mayor Mike Rawlings said in an interview after the Sutherland Springs shooting last year that the city had its hands tied by the Constitution. At the time, Caraway was toying with the idea of taking some action regarding the NRA meeting.

Rawlings last week instead focused on national leaders, writing a letter to President Donald Trump and Texans in Congress urging them to "summon the courage" to look for solutions for mass killings.

Other City Council members have also weighed in after the Florida shooting. Kevin Felder, who represents South Dallas and Far East Dallas, tweeted his opposition to the NRA convention.

Council member Rickey Callahan also wrote a letter to the mayor last week urging some type of local action and calling mental health the "800-pound gorilla in the room."

Caraway said Monday that mental health should be a concern, but gun violence must be addressed. He said he is not opposed to gun ownership — he claims he owns five guns — and supports the Second Amendment. But he said there is no reason for anyone to own an AR-15.

"We must get rid of these assault weapons to protect the children, and we must do something now," he said.

City columnist Robert Wilonsky contributed to this report.