Lawmakers in Albany consider how to make tight gun laws even tighter.

New York lawmakers are reviewing options to strengthen the state’s already muscular gun laws, with Gov. Kathy Hochul expected to unveil a package as soon as Wednesday aimed at shoring up remaining weaknesses in the aftermath of the Buffalo massacre.

At an appearance with President Biden in Buffalo on Tuesday, Ms. Hochul suggested that leaders should not merely blame “hateful philosophies” that she said had leached from dark corners of the web to mainstream cable news shows.

“You could have that hate in your heart, and you can sit in your house and foment these evil thoughts, but you can’t act on it — unless you have a weapon,” she said, adding: “That’s the intersection of these two crises in our nation right now.”

New York already has some of America’s strictest gun control laws, including requirements for background checks, restrictions on assault rifles, and red flag laws. New York has one of the lowest rates of gun death and injury in the country, according to the nonprofit New Yorkers Against Gun Violence.

In fact, one of New York’s most restrictive gun laws — which sharply limits the carrying of weapons outside the home — is being challenged in the Supreme Court, with a decision expected soon.

Even so, lawmakers say improvements under consideration in Albany could have great impact.

“You just want to close every potential loophole,” said Assemblywoman Amy Paulin of Westchester.

Ms. Paulin is the sponsor of a number of bills she believes would help make New York safer. One would require local law enforcement agencies to promptly contribute information on recovered weapons to a federal Bureau of Alcohol, Tobacco, Firearms and Explosives database, which would allow better tracing. Another would allow New York to do its own background checks, instead of outsourcing the process to the FBI.

Other measures would institute new requirements for gun dealers, including better record keeping and increased staff training.

But advocates have questioned whether New York’s existing laws could be better implemented.

Under New York’s so-called red flag law, for example, relatives, school officials and law enforcement can ask a court to remove guns from the home of a person at high risk of harming themselves or others and prevent them from buying new ones — a prohibition that can last as long as a year. But the law was not invoked against the suspect in the Buffalo attack, even after his threat to murder and commit suicide alarmed a school official enough to alert police.

“There was a breakdown here, but it wasn’t a breakdown of the law — it was a breakdown in implementation,” said John Feinblatt, president of Everytown for Gun Safety, a nonprofit that advocates against gun violence. He and others are pushing for more robust training for law enforcement and school administrators to know when to use the extreme risk law.

David Pucino, deputy chief counsel at the Giffords Law Center to Prevent Gun Violence, agrees.

“This really robust policy wasn’t used and it should have been,” he said. Mr. Pucino supports legislation that would limit the sale of guns to people under 21, similar to the one that Florida enacted after a 2018 mass school shooting in Parkland. But he stressed the challenge of addressing an issue like gun violence at the local level.

“No one law can be a solution to all problems,” Mr. Pucino said. “Especially a state law.”