Governments from London and Berlin to Jakarta and Tehran have spoken out against the move, which sparked havoc and protests at airports over the weekend, with some US-bound passengers turned away and others detained.
Mr Trump issued a statement reiterating that the order, which was partially blocked by a federal judge's ruling that stranded travellers could stay in the country, was "not a Muslim ban, as the media is falsely reporting".
"This is not about religion — this is about terror and keeping our country safe," he said, adding his policy was "similar to what President Obama did in 2011 when he banned visas for refugees from Iraq for six months".Mr Trump said the countries affected — Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen — had previously been identified by the Obama administration as being "sources of terror".
"We will again be issuing visas to all countries once we are sure we have reviewed and implemented the most secure policies over the next 90 days," he said, adding that he had "tremendous feeling for the people involved in this horrific humanitarian crisis in Syria".The President said America was "a proud nation of immigrants" and would "continue to show compassion to those fleeing oppression".
"But we will do so while protecting our own citizens and border," he added.
Mr Trump's chief of staff, Reince Priebus, had earlier defended the implementation of the action.
"It wasn't chaos," he said on NBC's Meet the Press program, adding that 325,000 travellers entered the US on Saturday (local time) and 109 of them were detained.
"Most of those people were moved out. We've got a couple dozen more that remain and I would suspect that as long as they're not awful people that they will move through before another half a day today."Asked why nations like Saudi Arabia, Afghanistan, Pakistan and Egypt were not included in the banned list, Mr Priebus said: "Perhaps other countries needed to be added to the executive order moving forward."