Kurt Nimmo, founder of the website inforwars.com, started the petition on the White House website, according to news reports.
The furor began after a particularly contentious interview between Morgan and Larry Pratt, the executive director of Gun Owners of America.
During the interview on his CNN show, "Piers Morgan Tonight," Morgan hammered Pratt and his defense of the 2nd Amendment and American gun laws.
"The argument I keep hearing is 'well if everybody else was armed, it wouldn't happen.' It's a load of total hogwash," Morgan told Pratt and other gun rights advocates who appeared on the show.
"How many more kids have to die, before you guys say, 'we want less guns, not more?'" Morgan added.
His comments came as Pratt and others discussed the recent Sandy Hook School massacre in Newtown, Connecticut, in which 27 people -- including 20 young children -- were shot by 20-year old Adam Lanza.
On Friday, National Rifle Association chief Wayne LaPierre said the answer to preventing mass shootings like the one in Newtown was to add armed guards to America's schools.
“The only thing that stops a bad guy with a gun is a good guy with a gun,” LaPierre said. “Would you rather have your 911 call bring a good guy with a gun from a mile away … or a minute away?”
His comments stoked intense controversy around the country and on Capitol Hill, where work is underway to reinstitute the federal ban on assault or military-style firearms.
Sen. Dianne Feinstein is leading the charge to get the ban, originally introduced into the U.S. code under the Clinton administration, back on the books.
The Newtown shootings are only the latest in a string of high-profile mass shootings in the United States in recent years.
In July, a lone gunman opened fire into a crowded movie theater in Aurora, Colorado. More than 70 people were shot and 12 died as a result of the rampage.
Last January, 2001, an Arizona man opened fire into a crowd gathered at an event held by former Rep. Gabrielle Giffords (D-Ariz.).The shooter killed six people during the incident, and Giffords was left with permanent injuries after being shot in the head.