The order, aiming to boost the country's security, has sparked controversy around the world and led to multiple protests in the United States.
"We denied boarding to 721 travelers that had visas from the affected countries," McAleenan stated on Tuesday.
The US Customs and Border Protection will process 872 refugees this week, he said.
"Eight hundred and seventy-two refugees will be arriving this week and we will be processing them for waivers through the end of the week."
Interagency communications on the implementation of US President Donald Trump’s executive order on immigration have not been smooth, he said.
"I think it is fair to acknowledge that communications…haven’t been the best in the initial rollout of this process…We are working with the State [Department] and the carriers [airlines] to make sure these folks know the rules."
