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, Fla., 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 Governor Rick Scott, a Republican weighing a US 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 Senator Steve Daines, a Montana Republican, 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, Utah’s Mike Lee and Kentucky’s Rand Paul, 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.
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 policy makers 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 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.
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.
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.
After four days of meetings with other governors and the group discussion with Trump, Governor Charlie Baker of Massachusetts said he “came away thinking that there was probably opportunity for action” on guns.
“There seemed to be fairly decent interest in expanding what’s in the NICS system and broadening the amount of information that is available through that,” he said, referring to the national background system.
“No one in that room was saying they should do nothing,” he said referring to a morning meeting at the White House. “Everybody in that room was saying they should do something and . . . it’s my hope that they do.”
Speaking to the Globe in a US Senate meeting room where he was about to participate in an event about opioids, Baker said he thinks federal officials “should reinstate the assault weapons ban,” which expired in 2004.
Baker said the ban is something he has “talked to a number of the governors down here about.” Baker has supported a federal reinstatement of the ban since at least late 2014. The state has long had a similar ban.
But in a TV interview before he was governor, Baker appeared to be much more reticent on reinstating the federal ban. “If I thought it would solve the problem, I’d be all for it,” he said on New England Cable News. “I need to see the evidence.”
Joshua Miller of the Globe staff contributed to this report.