Roger J. Stone Jr., an ally of President Trump and a self-proclaimed political “dirty trickster,” has been kicked off Twitter.In a series of tweets on Friday, Mr. Stone insulted several CNN news anchors and contributors. The messages appeared to be in response to reports that a federal grand jury had approved charges in the continuing investigation into the Trump campaign’s possible connections to Russia.Mr. Stone’s posts were littered with expletives. He said Don Lemon, the host of “CNN Tonight,” “must be confronted, humiliated, mocked and punished,” adding that he was a “buffoon.”He said Bill Kristol, a conservative pundit and a former columnist for The New York Times, was “packing on the pounds,” and used the hashtag #porky.He used an expletive to describe the political pundit Ana Navarro and wrote that Jake Tapper, who hosts “The Lead” on CNN, “must be held accountable for his lies and very severely punished.”Then his Twitter account was suspended, but there was some confusion. On Saturday, Mr. Stone wrote on Facebook that Twitter had notified him that the suspension would last only a few hours.But on Sunday, the account remained suspended. It was unclear whether that would be permanent. Mr. Stone told The Wrap he would sue Twitter. “The battle for free speech has just begun,” he said.“I have been inundated on Twitter with bloggers threatening to kill me, my wife, my kids and even my dogs, yet Twitter seems unconcerned about that,” he told The Wrap. “This is just part and parcel of the tech left’s effort to silence conservative voices.”Mr. Stone has since promised to speak out on other Twitter accounts, including those associated with his blog and the biographical movie “Get Me Roger Stone.” He has also started a petition calling for Twitter to reinstate his account.Emails sent to Mr. Stone via his blog, StoneColdTruth, were not answered immediately on Sunday.As a corporation, Twitter has the right to suspend accounts. A spokeswoman said on Sunday that she could not comment on any specific users but pointed to the company policy on abusive behavior.She highlighted the lines that said that users “may not incite or engage in the targeted abuse or harassment of others” and that an account may be considered abusive if it is “inciting others to harass another account.”There has been scrutiny over the company’s suspension policies given Twitter’s growing role in public discourse, especially because Mr. Trump uses it to bypass traditional news outlets and reach his supporters — and detractors — directly.Mr. Trump has tweeted to promote policies and to lob insults at various targets, including mainstream media organizations like The New York Times, politicians on both sides of the aisle, celebrities who criticize him and the mayor of San Juan, P.R.He has also retweeted images and videos with violent content, including one that showed him wrestling and repeatedly punching a man with a CNN logo imposed over his face, and another clip edited to show the president hitting a golf ball and striking his former campaign rival Hillary Clinton in the back.Some targets of Mr. Trump’s criticism have endured additional insults and threats from the president’s supporters, leading some to wonder whether the president has encouraged harassment and should be banned from Twitter himself.Mr. Stone left Mr. Trump’s campaign in 2015 amid widespread speculation about the reason for his departure.Mr. Trump said Mr. Stone was fired; Mr. Stone said he left voluntarily, suggesting that the candidate’s comments about the news anchor Megyn Kelly — comments that referred to “blood coming out of her eyes, blood coming out of her wherever” — had prompted his departure.But Mr. Stone remained loyal to the president and maintains that they still have a close relationship.On Monday, InfoWars published an article in which Mr. Stone said he urged Mr. Trump, in a “friendly phone call,” to release government documents about the assassination of President John F. Kennedy. Mr. Trump ordered the release of more than 2,800 of the documents on Thursday.