He did not provide evidence for this.
Critics accuse him of fomenting violence by using extreme and divisive rhetoric against opponents, the media, immigrants and Muslims.
Earlier this week Mr Trump offered condolences at a synagogue in Pennsylvania where 11 Jewish worshippers were shot dead at the weekend.
The White House has rejected any blame over the attack at the Tree of Life temple in Pittsburgh and the alleged gunman was not a Trump supporter.
However, a man arrested last week in connection with a mail-bombing campaign aimed at critics of Mr Trump had pictures of the president covering the windows of his van.
What did Trump say?
Addressing supporters in Estero, Mr Trump told them that the media “doesn’t want you to hear your story”.
“We have forcefully condemned hatred, bigotry, racism and prejudice in all of its ugly forms,” he said.
“But the media doesn’t want you to hear your story, it’s not my story, it’s your story.
“And that’s why thirty-three percent of the people in this country believe the fake news is in fact, and I hate to say this, in fact the enemy of the people.”
Mr Trump has regularly accused some sections of the media of misrepresenting his administration’s work.
In July the publisher of the New York Times urged him to stop calling reporters “enemies of the people”, saying it would “lead to violence” against the media.
What happened in Pittsburgh?
A gunman entered the Tree of Life temple during a service and fatally shot eight men and three women in what is thought to be the worst anti-Semitic attack in recent US history.
The suspect, who also wounded three police officers and was shot by them several times, has been named as Robert Bowers and faces 29 charges.
He had previously posted anti-Semitic content on the social network Gab and had also attacked Mr Trump, whom he called “a globalist, not a nationalist”.
What is at stake at the mid-term elections?
Voters are choosing new members of Congress, but how they vote will affect how the rest of Mr Trump’s presidency turns out.
Both houses of Congress are currently controlled by Mr Trump’s Republican Party.
The Democrats think they can win control of the House of Representatives this year by winning a majority of seats.
Doing so would let them block or delay the president’s plans by refusing to enact them.
Some opinion polls put the Democrats ahead in many places.