WASHINGTON — President Trump stopped short Monday of a full-throated endorsement of any legislative proposals to tighten gun restrictions while lawmakers insisted that the fate of any changes lay in the president’s hands.

While Senate leaders explored the possibility of passing a modest improvement to the national background-check system for firearm buyers, House action was uncertain, and Trump again turned attention away from guns and toward the various security breakdowns that preceded the Feb. 14 rampage inside Marjory Stoneman Douglas High School in Parkland, Florida, that left 17 dead.

Hosting dozens of governors at the White House on Monday, Trump reserved his harshest criticism for a local sheriff’s deputy who remained outside the school while Nikolas Cruz, the alleged shooter, targeted his former classmates and faculty members.

“You don’t know until you test it, but I think – I’d really believe I’d run into (the school), even if I didn’t have a weapon,” Trump said, telling the assembled governors that he thought they, too, would have rushed inside.

He did not, however, throw his support squarely behind any particular legislative proposal Monday, including measures he previously floated that would raise the minimum purchase age for rifles, mandate comprehensive background checks for gun buyers and ban “bump stocks,” which allow widely available semiautomatic rifles to fire like fully automatic guns.

Instead, Trump trumpeted his close ties to the leaders of the National Rifle Association, and he predicted that the powerful gun rights organization would “do something” to respond to the escalating concern nationwide about guns.

“Don’t worry about the NRA,” Trump said. “They’re on our side.”

In the wake of the shooting, a growing movement led by student survivors and parents has demanded tighter restrictions on firearms and pressured Trump and Congress to reject the NRA. Several lawmakers and governors – including Florida Gov. Rick Scott, a Republican weighing a U.S. Senate bid – have shifted away from NRA policy priorities and endorsed some hardening of state gun laws.

But a divided Congress that has a long track record of inaction after previous mass shootings is struggling to agree on any significant step with primary season getting underway.

“These are feel-good measures that aren’t going to solve the problem,” said Sen. Steve Daines, R-Mont., referring to age limits, bump stock bans and universal background checks.

The Senate could move on one modest but bipartisan gun measure backed by the NRA, the Fix NICS Act, which would create additional incentives and penalties to ensure that agencies report pertinent data on potential gun buyers to the National Instant Criminal Background Check System.

The bill was written to plug gaps exposed by the November killings of 26 churchgoers in Sutherland Springs, Texas, perpetrated by a man who would have been prevented from purchasing his weapons had the Air Force properly reported a 2012 domestic violence offense to the database.

Two Republican senators, Mike Lee, Utah, and Rand Paul, Ky., have registered objections to bill, warning that it “could lead to the denial of constitutional rights without due process.” A spokesman for Lee said Monday that he had placed a hold on the bill, blocking its rapid consideration.

It is unclear whether the House, which is scheduled to end its workweek Tuesday, would pass the bill as a stand-alone measure.

House lawmakers passed the Fix NICS Act in December, but as part of a bill that would require states to recognize concealed-carry permits from other states – a measure favored by the NRA but strongly opposed by gun-control advocates.

House Majority Leader Kevin McCarthy, R-Calif., appearing Monday on the Fox Business Network, called for action on background checks but did not specify whether he would bring the stand-alone NICS bill to the floor.

McCarthy said he had spoken to Trump over the weekend about potential action. “There are a number of actions he wants to take place,” he said. “You’re going to see more legislation.”

A bill aimed at beefing up background checks, first proposed in 2013 by Sens. Joe Manchin, D-W.Va., and Patrick Toomey, R-Pa., could be revived, the two men said, but they maintained that Trump’s support was a prerequisite.

“President Trump has to find a pathway that he feels comfortable with,” Manchin said in a Monday radio interview on West Virginia’s MetroNews network.

The Manchin-Toomey measure would mandate background checks for all gun sales between private parties, with exceptions for family members. Under current law, only federally licensed dealers must run checks, leaving many transactions exempt, including many conducted at gun shows and online.

Senate Minority Leader Chuck Schumer, D-N.Y., said Monday that “at the very least” Congress should pass legislation mandating universal background checks, similar to Manchin-Toomey, in response to the Parkland shooting.

“My Republican friends face a simple choice: Do something real on guns, or please the NRA. Doing both is impossible,” Schumer said.

There appeared to be waning enthusiasm among Republicans, and some Democrats, for a measure more closely tailored to the circumstances surrounding the Parkland shooting: a higher minimum age for rifle purchases.

Cruz, 19, bought his AR-15 rifle from a licensed dealer, passing a background check. Currently, long guns can be purchased at 18; some policymakers have floated raising the limit to 21, the current federal law for handgun buyers.

The NRA opposes raising the age limit, and lawmakers of both parties – including Manchin – have expressed concerns, often citing the fact that tens of thousands of 18-to-20-year-olds are entrusted with firearms as members of the military.

Democrats, meanwhile, are pushing to go further. Rep. Ted Deutch, D-Fla., who represents the district that includes the high school, co-introduced a bill Monday with Rep. David Cicilline, D-R.I., and more than 150 other Democrats to ban semiautomatic assault-style weapons, like the AR-15, that have military-style features.

Two other Democrats, Reps. Bill Pascrell, N.J., and Carolyn Maloney, N.Y., are set to introduce legislation Tuesday reimposing gun-purchasing restrictions on Social Security recipients who are unable to manage their benefits for mental health reasons – a rule that was overturned last year by the GOP-led Congress.

At the Monday meeting, Trump suggested he would act to regulate bump stocks even if Congress does not. The devices were not used in Parkland but were used by the gunman who killed 58 people last year in Las Vegas.

“I’m writing that out myself. I don’t care if Congress does it or not. I’m writing it out myself, OK?” Trump said to applause from some of the governors.

Even that would be tricky, with some questioning whether the Bureau of Alcohol, Tobacco, Firearms and Explosives has the authority to summarily ban the devices through regulations.

White House press secretary Sarah Huckabee Sanders said Trump had signed an executive order Monday “directing the ATF and Department of Justice to work on outlawing bump stocks so we don’t have to wait for a legislative fix.”

Sanders also said Trump favors “the concept” of raising the age to purchase some or all guns to 21, and she denied that the NRA had leaned on Trump to drop his previous vocal support for that idea. The president is waiting to see what Congress comes up with, she said: “A final determination and legislative piece has not been determined on that front yet.”

Trump, meanwhile, has discussed a host of responses apart from gun restrictions, ranging from a proposal to arm some teachers to calls for more aggressive restrictions on the gun rights of the mentally ill.

Trump directed his most pointed remarks at former Broward County sheriff’s deputy Scot Peterson, who remained outside the school during the Parkland massacre and resigned last week.

An attorney for Peterson on Monday denied that his client had acted unprofessionally or cowardly during the shooting. Joseph DiRuzzo said Peterson didn’t go inside the school because it had sounded as if the shooting was happening outside the building.

Trump said he wanted to make it easier for law enforcement to take guns from mentally ill people, saying police should have “immediate access” to their weapons.

The president also urged governors to revisit the closure of mental institutions, saying there should be a half-measure between institutionalization and leaving potentially dangerous people unsupervised.

“In the old days,” he added, it was easier to commit people to mental institutions if they acted “like a boiler ready to explode.”

Nevada Gov. Brian Sandoval, R, and Montana Gov. Steve Bullock, D, the chairman and vice chairman of the National Governors Association, met with reporters after the session at the White House and said they were more confident than in the past that this mass shooting would lead to action on school safety, guns and mental health issues.

“The president said this is number one on his agenda now, absolutely number one. I think it’s going to be the same for governors,” Sandoval said.

Bullock said, however, that the president’s proposal to arm teachers drew opposition from a number of governors.