The never-issued executive order would have also appointed a special counsel to pursue "criminal and civil proceedings."
The president has been pressured to act after two major mass shootings took 18 lives in March.
From border wall funds to the Muslim ban, the accomplishments Trump bragged about were done by executive action and have just as readily been undone.
Along with an executive order spree, the incoming president will review and freeze dozens of Trump-era rules and regulations.
Nebraska's Ben Sasse comes after Trump again after blasting his executive actions as "unconstitutional slop."
President Donald Trump attempted to sidestep Congress after negotiations between Democrats and Republicans remain at an impasse over new coronavirus aid.
Make Mexico pay for a border wall. Cut middle-class taxes by 35%. Bring jobs back from overseas. Trump has repeatedly failed to deliver on promises.
The administration could soon suspend certain migrants' rights to seek asylum in the U.S., drawing from the same legal authority as Trump's previous travel ban.
Trump signed the order while attending the annual convention of the American Farm Bureau Federation.