"We ask for early clarity from the US administration on the current situation," the International Air Transport Association (IATA) said in a statement.
On Friday, Trump signed an executive order barring US entry for travellers from seven mainly Muslim countries -- Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen -- for 90 days.
It also suspends the arrival of all refugees for at least 120 days, and Syrian refugees indefinitely.
The order led to chaotic scenes at airports around the world, as well as mass protests in major American cities and a diplomatic outcry.
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"It also placed additional burdens on airlines to comply with unclear requirements, to bear implementation costs and to face potential penalties for non-compliance."
IATA member airlines can be fined if they allow individuals who lack proper permits to board, and can be responsible for returning passengers who are denied entry to their point of departure.
Much of the chaos surrounding Trump's policy has been triggered by the fact that it affects dual nationals as well as those with valid US entry permits.