Donald Trump’s spokesperson, Sean Spicer, has denied making false assertions, insisting: “Our intention is never to lie to you.”

Spicer, 45, was catapulted to celebrity on Saturday when he launched a fierce attack on the media for its coverage of Trump’s inauguration. The press secretary claimed it had the biggest audience in history despite evidence from photos, crowd scientists, TV ratings and the Washington Metro network.

#SpicerFacts jokes flooded Twitter and were used with relish by public announcers at sports games across the US.

But on Monday, in his first question and answer session at the White House, Spicer was far from apologetic. He attempted to turn the tables on the media by pointing out errors in its own reporting.

Asked if it was his intention to always tell the truth from the west wing podium, Spicer replied: “It is. It’s an honour to do this and yes, I believe we have to be honest with the American people.”

In a curious remark, he added: “I think sometimes we can disagree with the facts ... But our intention is never to lie to you.”

Spicer, more amiable than when he delivered Saturday’s diatribe, said there are times when media organisations make mistakes and are forced to publish corrections. “We’ll do our best every time we can,” Spicer said. “I’m gonna come out here and tell you the facts as I know them.”

If a mistake is made, it will be corrected, he added. Apparently referring to his comment on Saturday that the White House will hold the media accountable, he said: “But as I said the other day, it’s a two-way street.”

Spicer backed down on his use of Metro statistics to back his claim about the inauguration crowd, but he stuck to his guns about the overall audience. “Sure, it was the most watched inaugural... There were tens of millions of people that watched that online... It’s unquestionable.”

This included on phones, TVs, tablets, on Facebook and YouTube, he argued. “I’d love to see any information that proves that otherwise... I don’t think there’s any question that it was the most watched inauguration ever. I think I’m right in saying [Ronald] Reagan didn’t have YouTube.”

Turning his fire on the media, Spicer criticised a mistaken media report that Trump had removed a bust of civil rights leader Martin Luther King from the Oval Office. “We have a tweet go out about Martin Luther King. Think about how racially charged that is... Where was the apology to the president of the United States?

“There’s a point at which we have a right to go out there and correct the record... We want to have an open and healthy dialogue with the press corps and the American people.”

Asked about the massive women’s marches in Washington and other major cities, Spicer said: “He has a healthy respect for the First Amendment. This is what makes our country so beautiful.”

The briefing room in the West Wing was as crowded as for Barack Obama’s farewell press conference five days earlier.

Sitting at his right side were White House staff including Trump counselor Kellyanne Conway and director of strategic communities Hope Hicks. He began with a broad grin and an upbeat, “Good afternoon, everyone!” – apparently from the Conway playbook.

Why did Spicer take no questions on Saturday? “I came out to read a statement,” he said. “I’m here today and I’m going to stay out here as long as you want. You guys might want to leave before I do.”