On Saturday the president had condemned media reporting of the number of people attending his inauguration.
White House Chief of Staff Reince Priebus said there was "an obsession... to de-legitimise this president. We're not going to sit around and take it."
But photos show more people attended the inauguration of Mr Trump's predecessor Barack Obama in 2009.
Mr Priebus said on Fox News Sunday that the "media from day one has been talking about de-legitimising the election". He said Mr Trump's presidency would fight such coverage "tooth and nail every day".
The latest row was mainly sparked by the inauguration figures.
There were no official estimates. Mr Trump said during a visit to the CIA on Saturday that it "looked like a million and a half people", but provided no evidence. He called reporters "among the most dishonest human beings on Earth" for saying it was far lower.
His press secretary Sean Spicer outlined figures amounting to 720,000 people in Washington's National Mall, despite also saying that "no-one had numbers" for the inauguration.
He also said it was the "largest audience to ever witness an inauguration - period - both in person and around the globe".
Many US outlets, using photos of the National Mall showing the difference in numbers attending the 2009 inauguration and Mr Trump's, hit out at Mr Spicer's statements.
The New York Times denounced "false claims" and described the statements as a "striking display of invective and grievance at the dawn of a presidency".
Both CNN and ABC News went into detail to refute Mr Spicer's claims.
Top Trump aide Kellyanne Conway also criticised the media in a feisty exchange on NBC.
She was challenged by Chuck Todd on NBC's Meet the Press to say why Mr Spicer's first appearance had been to "utter a probable falsehood".
"If we are going to keep referring to our press secretary in those type of terms, I think we are going to have to rethink our relationship here," she said.
Pressed on Mr Spicer's claims, she said he had been presenting "alternative facts".
"Alternative facts are not facts they are falsehoods," Todd replied.
Ms Conway insisted there was "no way to really quantify crowds" and, taking offence at a laugh from the reporter. said: "You can laugh at me all you want. It's symbolic of the way we are treated by the press the way you just laughed at me."
She also highlighted another issue that caused friction with the media - the Time Magazine reporter who incorrectly reported that a bust of civil rights hero Martin Luther King Jr had been removed from the Oval Office. The reporter later apologised for the error.
Mr Trump on Sunday tweeted about television ratings of the inauguration, saying that 31 million people had watched, 11 million more than four years ago.
He also referred to Saturday's day of protests that saw millions in the US and hundreds of thousands around the globe take to the streets in some 600 demonstrations against his presidency.
His initial tweet said he was "under the impression that we just had an election", asking: "Why didn't these people vote?"
A later tweet said that "peaceful protests are a hallmark of our democracy".
In other Sunday morning media exchanges:
- Kellyanne Conway told CBS programme Face the Nation that 20 million people relying on the soon-to-be-repealed Affordable Care Act known as Obamacare would not go without health care coverage during the transition to a new plan
- Ms Conway repeated that Mr Trump was "not going to release his tax returns"
- Reince Priebus said Mr Trump's first full week in office would focus on trade, immigration and national security
- Senior Trump ally Ted Malloch told the BBC that Nato would be reformed, with the possibility of "new institutions" and a definite focus on ensuring European members paid more towards the alliance