"Despite our differences on many issues, I believe there should be areas of agreement," the Vermont Democrat said during a committee hearing on Capitol Hill. "I want the committee to mark up legislation next month."
Leahy did not say what the bill might contain, but it is widely expected to include a proposal for "universal background checks" on all gun sales, including those sold at gun shows and sold privately.
"Universal background checks is a proven, effective step we can take to reduce gun violence," Sen. Chuck Schumer, D-N.Y., said at the hearing. "And I believe it has a good chance of passing."
The measure is also expected to include a gun-trafficking measure to stop "straw purchasers" from buying guns for people who can't pass a background check, Politico reported. In a straw purchase, a buyer lies about the identity of the ultimate possessor of the weapon.
The Senate legislation may also include provisions for better mental-health screening and better enforcement of existing federal gun laws, Politico said.
If the Democratic-controlled Senate passes a bill, it would then go to the Republican-controlled House.
Wednesday's Senate hearing began with former Rep. Gabrielle Giffords, D-Ariz., making her first formal statement on Capitol Hill since a shooting that nearly killed her two years ago.
"We must do something," she said in remarks of 72 words that she read slowly and carefully from a lined sheet of paper. "It will be hard. But the time is now. You must act. Be bold. Be courageous. Americans are counting on you."
Another witness was her husband, former astronaut Mark Kelly, who has joined her in advocating for stricter gun laws.
"Gabby's gift for speech is a distant memory," he said, referring to his wife by her nickname. "She struggles to walk, and she is partially blind." But "we aren't here as victims. We're speaking to you today as Americans," he said.
Other witnesses included a constitutional law professor, the Baltimore police chief, a pro-gun female lawyer who has pushed to keep assault weapons and high-capacity magazines available, and National Rifle Association Executive Vice President Wayne LaPierre.
LaPierre urged lawmakers to look at privacy laws "that needlessly prevent mental-health records from being included in the National Instant Check System."
But he disagreed with expanding background checks, saying that "you're never going to get criminals to go through universal background checks."
Leahy commented in the hearing that LaPierre supported universal background checks when he testified at a similar House hearing in 1999.
LaPierre later denounced a proposed assault-weapons ban as "based on falsehoods by people who don't understand firearms."
Notable deaths of 2014 [PHOTOS]
Korean War vet decorated 61 years after service