Trump on Friday signed an executive order suspending the arrival of all refugees for at least 120 days, Syrian refugees indefinitely -- and barring citizens from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen for 90 days.
The measures introduced a week after his inauguration were fiercely criticised over the weekend, although UN reactions were largely tepid.
The UN bodies most directly engaged with migration -- the UN refugee agency and the International Organization for Migration (IOM) -- issued a statement on Saturday which made no mention of the executive order and stopped far short of condemning it.
IOM spokeman Leonard Doyle on Monday dismissed suggestions that the Trump administration had threatened funding cuts if its policies were publicly criticised.
"I have heard nothing of the sort," Doyle told AFP.
According to IOM's website, the Geneva-based body receives funding from the US Agency of International Development and multiple divisions of the State Department but the details of those contributions were not immediately available.
Doyle said that in the aftermath of Trump's executive action the immediate concern was the protection of refugees whose resettlement process to the United States was ongoing.
"Suddenly they are back where they started or they are back several steps behind," Doyle said.
"We are worried about their immediate vulnerability," he added, noting that refugees who qualify for resettlement to the US or other developed countries have typically endured extreme hardships and have no prospect of safely returning to their home countries.
Asked if IOM would push Trump's government to reverse the new policy in the coming weeks, Doyle said, "we are hopeful that in the process of the review, when they have looked at every aspect of refugees, that things will return to an even keel."