In addition, a CNN poll found on Friday that 53 percent of Americans disapprove of the way Trump is handling his new job as president. "Sorry, people want border security and extreme vetting", the president writes on Twitter, in what has become his nearly daily morning series of tweets.
"I call my own shots, largely based on an accumulation of data, and everyone knows it", he wrote.
"Traditional phone polls that use live interviewers - including some of the most trusted polls in politics and media - report limited support for Trump and the controversial executive orders he's signed".
The firms - which include Apple, Facebook, Google, Microsoft and Twitter - said Mr Trump's executive order "inflicts significant harm on American business, innovation, and growth".
On Monday morning, the spirit moved Trump to make two statements about the polls he's been seeing.
The Justice Department is now fighting against a federal judge's ruling that halted Trump's travel ban on citizens of Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.
A poll from CBS News found that 51% of Americans disapprove of the ban, while 45% approve.
On Saturday, the US government suspended enforcement of the so-called travel ban after a federal judge in Washington state temporarily blocked the ban, marking an extraordinary setback for the White House.
Then he said, "What about that travel ban policy?"
Meanwhile, the executive order has been frozen by a legal challenge.