UN Secretary General Antonio Guterres has called for Mr Trump's ban on people from seven mainly Muslim countries entering the United States to be lifted "sooner rather than later".
Mr Trump's executive order last Friday halted the entire US refugee programme for 120 days, indefinitely banned Syrian refugees and suspended all nationals from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen from entering the US for 90 days.
He said it was to safeguard the US from terrorism.
But Mr Guterres, who was appointed to the UN's top position in October, said the measures were not an effective way of protecting countries from terrorists.
He called for the travel ban to be lifted as soon as possible, saying he did not believe it was the way to best protect the US or other countries from terrorism.
Border policies should not be based on religion, ethnicity or race and to do so was against the fundamental values and principles on which societies are based, he said.
Mr Guterres' comments were his first to directly address Mr Trump's signing of an executive order last Friday on immigration amid a drumbeat of criticism from around the world and protests.
Mr Guterres said travel bans risked playing to the advantage of terrorist organizations seeking to recruit members.
"If a global terrorist organization will try to attack any country like the United States, they will probably not come with people with passports from those countries that are hot spots of conflict today," he said.
He said such groups were likely to use people for attacks traveling on the passports of "developed and credible countries," or who had been living in the United States or other countries for decades.
The travel ban has been sharply criticised even by close American allies in Europe. The Arab League and the Organization of the Islamic Conference have denounced it.
Arab Gulf states remain quiet or approve of ban
Meanwhile, the rich Arab monarchies of the Gulf have been conspicuously absent from the chorus of international condemnation of the ban, hoping for warmer ties with Donald Trump than with his predecessor.
Saudi Arabia and its wealthy neighbours, Kuwait, the United Arab Emirates, Qatar and Bahrain, have traditionally been close US allies, and all were left off the travel ban which instead included their main regional rivals Iran, Iraq and Syria.
Of the five major oil monarchies, the only one to express even mild disapproval in public was Qatar, whose foreign minister was quoted during a visit to Serbia as saying he hoped Washington would reassess it.
Some Gulf officials even backed it openly. Dhahi Khalfan, a senior Dubai police official, tweeted on Monday "complete support" for Trump's ban. "Every country has the right to protect its security... Trump, what you're doing is right."
The Gulf states, ruled by Sunni Muslim monarchs and protected by the US Fifth Fleet, had troubled relations with previous US president Barack Obama, who they believed was too soft on their Shi'ite chief rival Iran.
In contrast Mr Trump repeatedly called Mr Obama "weak" on Iran and disparaged the outgoing administration's agreement to lift sanctions in return for curbs on Tehran's nuclear programme.
- RNZ / BBC / Reuters