President Donald Trump unleashed an early-morning attack Friday on CNN, tweeting at 3:14 a.m. that the "lowly rated" news organization can "criticize me at will," but when "I criticize them they go wild and scream, “it’s just not Presidential!”

Some argue Trump's rhetoric is partially to blame for attempted attacks – involving at least 12 bomb-like devices discovered in Washington, New York, Delaware, Florida and California – since many of the intended recipients of the suspicious packages are favorite targets of the president.

The White House has pushed back on the claim that Trump's rhetoric has caused violence, with Press Secretary Sarah Huckabee Sanders saying Trump "certainly isn't responsible" for the threats.

On Thursday evening, CNN's Jim Acosta tweeted to Trump's son, Donald Trump Jr., that "because of your father's rhetoric (calling us the enemy of the people), we are all very worried that somebody is going to get hurt."

And on Thursday night, CNN's Chris Cuomo mocked Sanders' defense of Trump with a quote from The Princess Bride.

“Presidential?” Cuomo said. “Sarah, you keep using that word. As Inigo Montoya said, ’You keep on using that word. I do not think it means what you think it means.”

Trump's Friday tweet came two days after CNN's New York offices were evacuated following the discovery of a suspicious package addressed to former CIA director John Brennan, who often appears on the network.

The package was one of the 10 addressed to liberal political leaders, including former President Barack Obama, former Secretary of State Hillary Clinton and former Vice President Joe Biden.

Trump on Wednesday initially pledged to "get to the bottom" of the suspicious packages. He also said that "in these times, we have to unify."

"We have to come together and send one very clear, strong, unmistakable message that acts or threats of political violence of any kind have no place in the United States of America," Trump said.

But at a Wednesday rally in Wisconsin, he argued that the media was responsible for sowing division in America. “The media also has a responsibility to set a civil tone and to stop the endless hostility and constant negative — and oftentimes, false — attacks and stories."

And on Thursday morning, Trump doubled down on his criticism of news organizations, tweeting that "a very big part of the Anger we see today in our society is caused by the purposely false and inaccurate reporting of the Mainstream Media."

CNN is a frequent target of the president, who has repeatedly denounced the network as "fake news" and occasionally tweeted videos depicting violence against its logo.

CNN President Jeff Zucker said Wednesday that the Trump administration doesn't appear to realize the effect of its rhetoric.

"There is a total and complete lack of understanding at the White House about the seriousness of their continued attacks on the media," Zucker said.

More:Total up to 12: Suspicious package to Sen. Booker recovered in Florida, another to Clapper

More:Potential bombs passed through Florida mailroom: What we know now about the 10 suspicious packages

More:White House denies that Trump's rhetoric to blame for suspicious packages, 'anger' in society