Such devices enable a rifle to shoot hundreds of rounds a minute.
Speaking at the White House, Mr Trump said he had directed the justice department to propose a law to make the accessories illegal.
The gun control debate took on a new urgency after 17 people were killed at a school in Florida last week.
Students and parents affected by the massacre at Marjory Stoneman Douglas High School are planning a demonstration in the state capital of Tallahassee on Wednesday.
Some of them arrived on Tuesday in time to see the state legislature reject a proposed ban on assault weapons and large capacity magazines. However, it will consider a package of more limited gun restrictions.
More about: Trump