The Oscar-winner Inarritu appeared to take aim at the new US President before he presented the award to Chazelle for best feature film director. Although none of them mentioned Trump by name, according to The Hollywood Reporter.
"As a filmmaker, as a Mexican, as a human being first and foremost, I feel incredibly proud, honored and humbled to have been recognized by this amazing, inclusive and diverse guild," Inarritu said on stage.
Villeneuve, the French-Canadian director of Oscar-nominated film "Arrival", referred on stage to Trump's controversial travel ban.
"In the morning the first thing I do is go on Twitter to see if my visa is still legal," he said.
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He later drew applause when he said "as a foreigner, I never felt as welcome and respected as I have been in the United States."
Trump has signed the executive order to suspend entry of refugees to the US for 120 days, and imposed an indefinite ban on refugees from Syria. A 90-day ban was also placed on citizens of seven predominantly Muslim countries, including Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.