The brief says the President's executive order offends "principles of fairness and predictability" and therefore "inflicts significant harm on American business, innovation, and growth as a result".
Tech companies have been among the most vocal critics of the ban, despite some of the leaders of the companies, including Apple chief executive Tim Cook, having publicly met with Trump.
Trump's executive order banning nationals from seven Muslim-majority countries – Iraq, Iran, Syria, Somalia, Sudan, Yemen and Libya – sparked a wave of protests across America and around the world.
A flurry of court rulings has left the ban in limbo, after it was ruled unconstitutional by a Seattle court. The tech companies are aligning themselves against the ban in court, although they will not be involved in the litigation.
Trump earlier told followers to blame the judge who ruled his order unconstitutional for future terrorist atrocities. He said: “If something happens blame him and court system.”
Just cannot believe a judge would put our country in such peril. If something happens blame him and court system. People pouring in. Bad!— Donald J. Trump (@realDonaldTrump) February 5, 2017
Over the weekend Trump repeatedly criticised the judge who ruled against his ban over Twitter, saying he was “opening up our country to potential terrorists” and putting the country in “such peril”.