The measures would include support for tougher background checks for buyers under the age of 21 and cracking down on illegal gun purchases.
Crucially, the proposals are supported by 10 Republicans, meaning they have the numbers to be voted into law.
President Biden said the plans were "steps in the right direction" but they fall far short of what he called for.
Tens of thousands of protesters rallied across the US on Saturday to call for stricter gun laws in the wake of two mass shootings.
