The US Supreme Court ruled on Monday to allow part of the ban which applies to citizens and refugees from Iran, Libya, Somalia, Sudan, Syria, and Yemen.
Visa applicants from the six countries must have a close US family relationship or formal ties to a US entity to be admitted to the United States under guidance distributed by the US State Department on Wednesday.
"The airline continues to accept nationals with valid travel documentation from the six listed countries," an Etihad Airways spokesman said in a statement. "Acceptance, as per standard procedure, is subject to checks completed by US authorities at the preclearance facility at Abu Dhabi airport."
Emirates, the Middle East's largest airline, earlier said its flights to the United States were "operating as per normal" after the United States announced new travel restrictions.
The United States has also released new security measures for inbound flights that are designed to prevent expanding the in-cabin ban on laptops.
"Our flights to the US are operating as per normal. All passengers must possess the appropriate travel documents, including a valid US entry visa, in order to travel. Emirates remains guided by the US Customs and Border Protection on this matter," an Emirates spokeswoman said in a statement.
Etihad flies to six US cities. Emirates flies to 12.