“It was absolutely surprising and stunning,” the president of the White House Correspondents’ Association, Jeff Mason, said on CNN on Sunday.

The tensions flared anew on Sunday when Kellyanne Conway, one of Mr. Trump’s top advisers, said in a television interview that Mr. Spicer had merely presented “alternative facts” about the inauguration, prompting an astonished response from her questioner, Chuck Todd of NBC.

“Wait a minute — ‘alternative facts’?” Mr. Todd asked Ms. Conway on “Meet the Press.” “Look, alternative facts are not facts. They’re falsehoods.”

When Mr. Todd pressed her about why the administration had put Mr. Spicer behind the lectern for the first time to “utter a provable falsehood,” Ms. Conway responded with a sharp threat. “If we’re going to keep referring to our press secretary in those types of terms, I think that we’re going to have to rethink our relationship here,” she said.

Video of Ms. Conway’s evasion quickly spread on social media. The phrases “alternative facts” and “#alternativefacts” had been used on Twitter more than 380,000 times by midafternoon on Sunday, a Twitter spokesman said.

Also by Sunday afternoon, there were scattered calls for the White House press corps to boycott Mr. Spicer’s briefings, although such a drastic response appeared unlikely.

Ben Smith, the editor in chief of BuzzFeed, said on Sunday that the briefings were “a useful, if not essential, tradition” and that his outlet would keep a reporter there. Mr. Smith added that the Trump administration would “find practical reasons to be honest.”

“In particular,” Mr. Smith wrote in an email, “I think they’ll find in moments of real crisis, rather than political theater, that they need to win back the credibility that they are spending now.”

Mr. Mason, the correspondents’ association president, who is the chief liaison between the White House press corps and Mr. Spicer, said his goal was to maintain a constructive relationship.

“It’s up to him and up to the president to decide how they want to get started,” Mr. Mason said of Mr. Spicer. “And that’s what they decided.”

Some reporters and commentators noted that hostility between White House press operations and the news media was nothing new.

Jack Shafer, the acerbic media critic, wrote on Twitter that “the press is supposed to be abused, disparaged, defamed, dissed.” He added, “It’s part of the job.”

Lynn Sweet, a political reporter for The Chicago Sun-Times, said credibility, not civility, was what mattered.

“If Sean wants to have an angry tone, frankly, I don’t care,” Ms. Sweet said on CNN. “I don’t care if you vent.”

She added: “I care if he says something that’s true. I care if he gives us facts.”

In an interview on Sunday, Ari Fleischer, who served as press secretary under George W. Bush, said that Mr. Spicer’s statements on Saturday were somewhat typical of the spin at press briefings.

But Mr. Spicer’s “eagerness and willingness” to confront the press corps so directly represented a break from tradition, Mr. Fleischer said. “Everybody complains about the press, but most people bite their tongue” in news conferences, Mr. Fleischer said.

Mr. Fleischer added that Mr. Spicer’s remarks could hurt his credibility unless he backed them up — or at least addressed them — during the first official White House briefing on Monday.

“Sean’s first client is the president of the United States and those around the president; his second client is the press corps,” Mr. Fleischer said. “And he has to serve both, always guided by the truth.”

In reporting on the day’s events, many news organizations also called out the falsehoods that Mr. Trump and Mr. Spicer offered on Saturday, using variations of “false,” “falsehoods” and “lies” in headlines and stories. Breitbart News, the right-wing website that has embraced Mr. Trump, was more credulous in its headline: “WH Press Secretary Sean Spicer Blasts Media’s ‘Deliberately False Reporting.’”

Voice of America, the government-funded news operation that broadcasts American journalism beyond the country’s borders, pointed out Mr. Spicer’s inaccuracies and ran an article from The Associated Press fact-checking his remarks.

Still, that came only after the organization initially posted a string of Twitter messages that quoted Mr. Spicer without context, prompting questions about whether it was endorsing his comments. Voice of America’s director, Amanda Bennett, said that there had been no instructions or interference from the Trump administration and that Voice of America had quickly decided it needed to provide more explanation.

“Internally, there was like an explosion of direct messages saying you’ve got to do something about this,” Ms. Bennett said in an interview on Sunday.

That led to a course correction on Twitter, including the deletion of one tweet that appeared to support Mr. Spicer.

For First Amendment advocates, the events of Mr. Trump’s first 48 hours in office were, to say the least, unsettling.

In a statement, the American Civil Liberties Union denounced Mr. Spicer’s remarks as “possible government censorship” and vowed that any threats by Mr. Trump’s administration to the principles of freedom of the press would be met with a “vigorous defense” of the First Amendment.

“If Trump wants to take on the First Amendment,” the group said in the statement, “we will see him in court.” New York Times