Story highlights "Well, this is something that we're looking at" McMaster said

This renewed discussion of the travel ban comes after Friday morning's terror attack in London

Washington (CNN) The Trump administration is considering a new travel ban to replace its original executive order, which has had its legality questioned and is up for a Supreme Court hearing next month, White House national security adviser H.R. McMaster said Sunday.

"Well, this is something that we're looking at, is how to protect the American people better, how to ensure that we know who these people are who are moving," McMaster told George Stephanopoulos on ABC's "This Week."

NSA McMaster tells @GStephanopoulos that a new travel ban "is something that we're looking at." #ThisWeek pic.twitter.com/rxisKa68S1 — This Week (@ThisWeekABC) September 17, 2017

This renewed discussion of the travel ban comes after Friday morning's terrorist attack in London, in which 30 passengers on a London Underground train were injured after a bomb went off.

In a tweet Friday in response to the attack , President Donald Trump called for a "larger, tougher and more specific" travel ban and also called for shutting down terrorist group's use of the internet for indoctrination and recruitment.

The travel ban into the United States should be far larger, tougher and more specific-but stupidly, that would not be politically correct! — Donald J. Trump (@realDonaldTrump) September 15, 2017

Loser terrorists must be dealt with in a much tougher manner.The internet is their main recruitment tool which we must cut off & use better! — Donald J. Trump (@realDonaldTrump) September 15, 2017

McMaster echoed the point Sunday.