Negotiations have narrowed proposals to address school safety, standards for safe gun storage, federal support for mental health programs and incentives for states to create red flag laws.
The president said the upper chamber needs to pass legislation approved by the House earlier this month, which would tighten gun laws including background checks.
The FBI's National Instant Criminal Background Check System set a record in June with 3.9 million background checks. The previous record of 3.7 million background checks was set in March.
The group says its plan could prevent 200,000 gun deaths over 10 years. It calls for creating a national registry and starting a buyback program and creating a national gun czar.
Governor Roy Cooper signed a new gun safety Executive Directive on Monday. It aims to strengthen background checks among other things.
President Trump says he supports "really intelligent background checks." It's unclear what exactly that means, but support for universal background checks is near universal among Americans.
Senate Majority Leader Mitch McConnell isn't budging on his opposition to a bill expanding background checks. But other GOP lawmakers who opposed earlier restrictions are now saying it's time to act.
Ohio's Republican governor is proposing new gun control laws in response to the deadly mass killings in Dayton. This would be a big change for the Ohio GOP if he gets his way.
Gun control groups say the National Rifle Association has been "distracted" by recent investigations, financial troubles and turnover. But the organization clearly still holds sway in Washington, D.C.