Reince Priebus, the president's chief of staff, said during an interview on ABC's "This Week" on Sunday that the White House has discussed potential changes to laws that are intended to safeguard free speech.
"How it gets executed or whether that goes anywhere is a different story," Priebus said. But he added that he thinks "newspapers and news agencies need to be more responsible with how they report the news."
Related: Trump calls for changes to libel laws in attack on New York Times
Changing the laws wouldn't be easy. Libel laws vary by state, and there's no federal libel law. And weakening press freedoms would likely take a constitutional amendment.
Trump and his administration have made attacks on the media a recurring part of his platform. Changing libel laws was even part of Trump's campaign trail rhetoric.
In February 2016, Trump said if he won the presidency he would "open up our libel laws so when (media) write purposely negative and horrible and false articles, we can sue them and win lots of money."
Trump has frequently revisited the issue while attacking one of his favorite media targets -- The New York Times.
"We're supposed to be tough, we're supposed to ask him hard questions. I'm not sure he gets that," Baquet said. "The more he beats us up, to be frank, I think that's bad for the country. I think it's bad for the free flow of information and criticism."
CNN contributor Carl Bernstein, who broke the Watergate case as a reporter for the Washington Post, said Sunday on "Reliable" that Trump's recent tone toward the press has been "venomous."
Trump decried the mainstream media during a rally Saturday in Pennsylvania that he held to tout the accomplishments of his first 100 days in office.
"We have a president who doesn't understand the Constitution, who is ignorant of (the media's) history," Bernstein said. "He deserves our respect as the duly elected president of the United States. That does not mean he does not deserve to be called out when he lies."
--CNNMoney's Tom Kludt contributed to this report.
Yesterday on Twitter, President Trump complained about The New York Times (which he had previously identified as an "enemy of the American People") and suggested that its coverage could be improved by making it easier for public figures like him to file successful defamation lawsuits: "The failing @nytimes has disgraced the media world. Gotten me wrong for two solid years. Change libel laws?" The tweet recalled comments Trump made during his presidential campaign last year, when he said, "I'm going to open up our libel laws" so that "when The New York Times writes a hit piece which is a total disgrace or when The Washington Post...writes a hit piece, we can sue them and win money instead of having no chance of winning because they're totally protected."
As New York Times legal writer Adam Liptak points out (not for the first time), the president actually has no power to "open up our libel laws," since libel "is a state-law tort, meaning that state courts and state legislatures have defined its contours." Furthermore, the Supreme Court has said the First Amendment limits the ability of politicians and other public figures to recover damages when a journalist makes them look bad: They have to show not only that a reputation-damaging story was false but that the author knew, or at least suspected, it was false. That "actual malice" standard has been the law for more than half a century, since the Court decided New York Times v. Sullivan. "Changing New York Times v. Sullivan would require either the Supreme Court to overrule it or a constitutional amendment," Liptak writes. "Neither is remotely likely."
Yesterday's tweet shows that Trump's misunderstanding of libel law goes beyond his ignorance of how it is made and how it is constrained by the First Amendment. His tweet links to a piece in which New York Post columnist John Crudele criticizes the Times for omitting relevant information from its coverage of Trump's widely derided claim that "President Obama was tapping my phones in October." Crudele notes that the Times reported last January, under the print headline "Wiretapped Data Used in Inquiry of Trump Aides," that "American law enforcement and intelligence agencies are examining intercepted communications and financial transactions as part of a broad investigation into possible links between Russian officials and associates of President-elect Donald J. Trump." Trump says that article confirms his claim about Obama. It doesn't, as Crudele concedes. But he argues that the story "does make Trump's accusation look a little less crazy" and should have been mentioned in coverage of the controversy about Obama's alleged wiretapping of Trump Tower.
Even if you think Crudele has a point, there is nothing remotely libelous about the articles he is criticizing. They may be incomplete, but they are not defamatory, because they are not false. As evidence of the need to "change libel laws," Trump cites unfavorable press coverage that is accurate but arguably lacks context. Even if New York Times v. Sullivan had never happened, such a complaint would not justify a libel claim, which has to assert that the defendant said something that was verifiably false. Without that threshold requirement, journalism would be financially untenable, because disagreements about its quality would be resolved through litigation instead of criticism and public debate.
Trump does not seem to grasp that journalism can be not just negative but unfair, unbalanced, or misleading without being libelous (which helps explain why he threatens to sue people at the drop of a hat). When he complains that the Times has "gotten me wrong for two solid years," he may mean that the paper underestimated him, that it consistently portrayed him in a negative light, or that he did not recognize himself in its coverage. None of that is grounds for a lawsuit, and anyone who values freedom of speech should be thankful for that fact.
In a tweet Thursday morning, Trump shared a column that sharply criticized the New York Times' coverage of him.
"The failing @nytimes has disgraced the media world," Trump said. "Gotten me wrong for two solid years. Change libel laws?"
Trump said multiple times on the campaign trail last year that he would be in favor of changes to libel laws, a dramatic escalation from his typical anti-media rhetoric.
A year ago in February, Trump said that, as president, he would "open up our libel laws so when they write purposely negative and horrible and false articles, we can sue them and win lots of money."
In late October, Trump said that America's press protections went too far and should more closely resemble British law.
"In England you have a good chance of winning. And deals are made and apologies are made," he said at the time.
Related: Trump wants to 'open up' libel laws so he can sue press
Under British law, the burden of proof is on the defendant to prove that a statement was true.
In America, the burden is on the plaintiff, the result of the landmark 1964 Supreme Court case "New York Times vs. Sullivan," which required public figures who are suing news organizations for libel to prove that false information was published knowingly and with malicious intent.
Trump's comments last year unsettled much of the news media, and journalists were similarly irritated by his tweet on Thursday.
But it wouldn't be easy for Trump to "change" or "open up" the laws. For one thing, there is no single law that could be changed, other than the First Amendment and the protections it gives. Libel laws vary by state; there is no federal libel law.
A White House spokeswoman did not respond to an inquiry seeking more information on the president's thinking.
Trump's tweet was his second attack on the "failing" New York Times in as many days. On Wednesday, he falsely claimed that the newspaper "apologized to its subscribers, right after the election, because their coverage was so wrong." In fact, the Times made no apology.
Related: Trump says NYT 'failing' -- but stock up 30% since election
On Thursday, Trump tweeted out a three-day old column published by the New York Post's John Crudele, who wrote that he canceled his subscription to the Times due to what he said was dishonest coverage of the president.
Last month, First Lady Melania Trump settled her own defamation lawsuit against a Maryland blogger who wrote that she used to be involved in a "high-end escort" service.
She had also sued the parent company of the British tabloid the Daily Mail for publishing the same claim.
The Daily Mail retracted its story after the lawsuit was filed, and the case was tossed last month over jurisdictional issues. The first lady refiled the lawsuit days later.