The president said the "consequences would be devastating" if the former judge challenges Democratic Sen. Doug Jones in 2020.
"The American public has a right to hear directly from him," the Louisiana senator said in a statement.
Certain states and localities would need to get clearance from the Department of Justice before abortion laws could go into effect.
The 2020 presidential hopeful called Trump's medical deferment for bone spurs “an assault on the honor of this country.”
Some advocates are worried that efforts to raise the legal smoking age to 21 are being used as a "Trojan horse" for large tobacco companies.