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.
In all around 100 students, spread across three buses, made the journey of more than seven hours to the state capital.
For many of these students, it is their first time to the capitol building in Tallahassee – much less to lobby their lawmakers over a national issue.
There is an excitement among the students, who sense that they may be on the cusp of starting a national movement.
“We’re travelling to our state capital to make sure that none of these people that we grew up with – that we’ve known our whole lives – die in vain,” Julia Salomone, 18, said confidently.
So how do the students expect the politicians to receive them? “Honestly, I feel like they’re gonna be overwhelmed by us because they’re going to see in our faces our determination, our commitment to this, because this is all we’re fighting for right now,” 16-year-old Rain Valladares said. “They’re gonna look us in the face and see that we’re not gonna back down.”
At an event on Tuesday recognising the bravery of law enforcement, Mr Trump said he had directed Attorney General Jeff Sessions to finalise new guidelines to declare bump stocks illegal “very soon”.
“The key in all of these efforts, as I said in my remarks the day after the shooting, is that we cannot merely take actions that make us feel like we are making a difference, we must actually make a difference,” he said.
“We must move past clichés and tired debates, and focus on evidence-based solutions and security measures that actually work and that make it easier for men and women of law enforcement to protect our children and protect our safety.”
Both Democrats and Republicans agreed in the nationwide wave of horror following the Las Vegas attack that the sale of bump stocks should be outlawed. (Courtesy BBC)