Morgan went head-to-head with radio host Alex Jones, who created the petition, during Monday evening's (January 7) edition of Piers Morgan Tonight on CNN.
White House spokesperson Jay Carney has now issued a statement saying: "The White House responds to all petitions that cross the [25,000-signature] threshold and we will respond to this one.
"In the meantime, it is worth remembering that the freedom of expression is a bedrock principle in our democracy."
Morgan made his calls for gun control after 26 people - including 20 children - were killed at Sandy Hook Elementary school in Connecticut.
The broadcaster has continued to defend his viewpoint and has since called for a ban on assault weapons and high-capacity magazines.
Over 100,000 people are now believed to have signed the petition.
Watch Piers Morgan and Alex Jones on the January 7 edition of Piers Morgan Tonight below: