In the interview, Fox said that although the number of mass shootings has risen in recent years, there are too few to draw a clear trend line. He accused the media of causing unnecessary panic.
“There is no evidence that we are in the midst of an epidemic of mass shootings,” Fox told interviewer Nick Gillespie.
The tweet that Trump shared providing a link to the interview was written by Fox News Channel host Laura Ingraham. It was among a spate of retweets by Trump on Thursday morning on varied subjects.
The White House did not immediately respond to a question about what message Trump was trying to convey by sharing the tweet.
In an email to The Washington Post on Thursday, Fox said he was not suggesting that nothing be done about gun violence.
“The big problem is the 11,000 victims killed annually by gunfire,” he said.
In the wake of the recent mass shootings in El Paso and Dayton, Ohio, that killed 31 people, Trump has vowed to push Republicans to embrace legislation that would strengthen background checks for gun buyers and persuade the National Rifle Association to drop its long-standing opposition to such measures.
Last week, Trump told reporters at the White House that conversations in recent days had yielded strong congressional support for “very meaningful background checks” and that his party, which has stymied gun-control efforts this year by Democrats, would take the lead in passing legislation after returning from an August recess.
“I think Republicans are going to be great and lead the charge, along with the Democrats,” Trump said.
He continued to express support for stronger background checks when speaking to reporters on Tuesday in New Jersey.
According to a Post analysis published this month, four or more people have been killed in a mass shooting every 47 days, on average, since June 17, 2015. That was the evening a young white supremacist killed nine people during a Bible study at a historic African American church in Charleston, S.C.
During the podcast, Fox said some in the media have contributed to an “obsession” with mass shootings by using a definition that overstates the carnage. In his research, Fox said, he defines a “mass killing” as episodes in which four or more people, excluding the shooter, are killed. Such instances are rarer than when four or more are shot, he said, given that only a fraction of those who are shot die.