A CNN/ORC poll released on Sunday found that 53 per cent of American respondents opposed Trump's Muslim travel ban.
On January 27, Trump issued a blanket ban on all travellers from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen for 90 days.
CNN's Brian Stelter pointed out that Trump tweeted about "fake" polls about 30 minutes after the network revealed the poll results.
It comes as The New York Times released an unflattering portrait of Trump's nights at the White House.
It suggested he spends much of his time watching cable news and wasn't fully briefed before signing an executive order elevating Stephen Bannon to the National Security Council.
SEAN SPICER REACTS TO SNL PARODY
Actress Melissa McCarthy's hilarious impersonation of White House press secretary Sean Spicer on Saturday Night Live made headlines around the world.
Now Spicer has responded to the parody, calling it "cute" and "funny".
"It's part of American culture," he told Fox & Friends on Sunday, adding that he received "a lot of texts" after the skit aired.
"Walking out of church, I looked down. There's a lot of texts this morning," Spicer said. "I had to click on the link and see what it's all about."
PUTIN DEMANDS APOLOGY
The Kremlin has demanded an apology from Fox News over what it said were "unacceptable" comments one of the channel's presenters made about Russian President Vladimir Putin.
Fox News host Bill O'Reilly described Putin as "a killer" in the interview with Trump as he tried to press the US president to explain more fully why he respected his Russian counterpart. O'Reilly did not say who he thought Putin had killed.
"We consider such words from the Fox TV company to be unacceptable and insulting, and honestly speaking, we would prefer to get an apology from such a respected TV company," Kremlin spokesman Dmitry Peskov told reporters on a conference call.
Trump, when commenting on the allegations against Putin in the same interview, questioned how "innocent" the United States itself was, saying it had made a lot of its own mistakes. That irritated some Congressional Republicans who said there was no comparison between how Russian and US politicians behaved.
Putin, in his 17th year of dominating the Russian political landscape, is accused by some Kremlin critics of ordering the killing of opponents. Putin and the Kremlin have repeatedly rejected those allegations as politically-motivated and false.
TRUMP 'BLAMES OBAMA PEOPLE FOR LEAK'
President Trump has blamed "Obama people" for the embarrassing leaks of contentious private phone calls he's had with the leaders of Australia and Mexico.
"It's a disgrace that they leaked because it's very much against our country," Trump told Fox News, blaming civil servants loyal to the former president for the leaks. "It's a very dangerous thing for this country."
Trump vowed to replace the White House and National Security Council staff that were holdovers from the Obama administration with his own people.
He disputed the characterisations of the phone calls, insisting in the interview that his conversations with Mexico and Australian Prime Minister Malcolm Turnbull were "positive."
