WASHINGTON—President Trump signed an executive order Friday directing the government to review rules requiring retirees to start taking annual withdrawals from retirement funds after they turn 70 ½ and to consider making it easier for small businesses to offer employees 401(k) plans.

The action, signed during a ceremony in Charlotte, N.C., ahead of the Labor Day weekend, was billed by the White House as a push to better prepare workers for retirement.

As...