– Gov. Mark Dayton said Monday that he's willing to consider any proposals that could protect Minnesota children from school shootings — up to and including arming school staff.

Dayton, in Washington for a gathering of the National Governors Association, said he would meet Tuesday back in Minnesota with his agency heads to discuss how to make schools more safe.

"I asked my Cabinet members to put their thinking caps on," Dayton said, after he and 38 other governors met with President Donald Trump at the White House. "Everybody agrees we want schools to be safe for students, for teachers. … I'm open to anything and everything at this point."

At the White House, the president pitched his own ideas, ranging from a ban on bump stocks to arming teachers, coaches and other school staff members.

"I don't rule anything out," said Dayton, speaking by phone after the meeting. "I'd want to talk to the teachers and educators in Minnesota, see what their perspective is on it."

The governor said local school officials might be in the best positions to talk about the needs and risks at individual schools, an idea echoed by Republican lawmakers in Minnesota, where school safety was also on the agenda. At a news conference to discuss their 2018 legislative priorities, senators said they would like to give local school officials more money to improve security as they see fit.

"It's high time that we look at how we can make our schools safe and secure for our students," said Sen. Carla Nelson, R-Rochester, who chairs the Senate's E-12 Finance Committee.

Nelson said she's been talking to law enforcement officials who told her to "harden the target," and to school leaders, who said they do not want a top-down solution. She introduced a bill Monday that would designate funding that schools could use for such things as armed security guards, cameras or bullet-resistant glass.

Sen. Eric Pratt, chairman of the E-12 Policy Committee, said he's looking into changing the state law that requires students to evacuate a building when a fire alarm is pulled. In the Parkland, Fla., shooting where 17 people were killed, the gunman triggered the fire alarm to get students to leave their classrooms.

As for arming teachers, Pratt, R-Shakopee, said that is not an approach he is currently interested in.

"I don't see that as something I'm going to be taking up in my committee right away," said Pratt.

DFL legislators, meanwhile, are pushing for universal background checks. They also want family members and law enforcement to be able to ask courts to remove someone's guns if they are a danger to themselves or others.

Senate Majority Leader Paul Gazelka, R-Nisswa, said he's willing to look at "any idea that actually works."

He and Nelson said they are waiting to hear the latest state budget forecast on Wednesday before deciding how much money to pursue for school safety and exactly where the cash will come from.

During his meeting with the governors, the president vowed to turn the nation's "grief into action" after the mass school shooting in Parkland. While "our nation is heartbroken," he said, the U.S. must "have action" on measures related to school safety and gun violence.

Trump said his recent call for the arming of teachers wasn't a universal one, but suggested that school employees with proper training and athletic ability could help protect students.

"The headline was 'Trump wants all teachers to have guns. Trump wants teachers to have guns.' I don't want teachers to have guns," the president said. "I want highly trained people that have a natural talent, like hitting a baseball or hitting a golf ball or putting."

The president also found fault with the officers who lingered outside the school during the gunman's rampage. The deputies, he said, "weren't exactly Medal of Honor winners" and Trump suggested he would have behaved differently.

"I really believe I'd run in there even if I didn't have a weapon," he said.

White House spokeswoman Sarah Huckabee Sanders later walked back the president's remark, telling reporters, "He was saying that he would be a leader and would want to take a courageous action, and a lot of the individuals that helped protect others that day weren't carrying firearms, which I think shows that you can be helpful in that process."