"President Trump's Executive Order affects a minor portion of international travelers, and is a first step towards reestablishing control over America's borders and national security," the statement read.
"Approximately 80 million international travelers enter the United States every year. Yesterday, less than one percent of the more than 325,000 international air travelers who arrive every day were inconvenienced while enhanced security measures were implemented. These individuals went through enhanced security screenings and are being processed for entry to the United States, consistent with our immigration laws and judicial orders.
"The Department of Homeland Security will faithfully execute the immigration laws, and we will treat all of those we encounter humanely and with professionalism. No foreign national in a foreign land, without ties to the United States, has any unfettered right to demand entry into the United States or to demand immigration benefits in the United States.
"The Department of Homeland Security will comply with judicial orders; faithfully enforce our immigration laws, and implement President Trump's Executive Orders to ensure that those entering the United States do not pose a threat to our country or the American people."
"The Department of Homeland Security will faithfully execute the immigration laws, and we will treat all of those we encounter humanely and with professionalism. No foreign national in a foreign land, without ties to the United States, has any unfettered right to demand entry into the United States or to demand immigration benefits in the United States.
"The Department of Homeland Security will comply with judicial orders; faithfully enforce our immigration laws, and implement President Trump's Executive Orders to ensure that those entering the United States do not pose a threat to our country or the American people."
"Nothing in the Brooklyn judge's order in any way impedes or prevents the implementation of the president's executive order which remains in full, complete and total effect," Miller said.
Miller was referring to U.S. District Judge Ann Donnelly from New York who issued the emergency order after lawyers for the American Civil Liberties Union filed a court petition on behalf of several refugees who were detained across multiple airports across the U.S., hours after the ban went into effect.
Following President Trump's executive order, anyone arriving into the U.S. -- even with a valid visa from Iraq, Syria, Iran, Sudan, Libya, Somalia, and Yemen -- could be denied entry into the country. While President Trump earlier said that the ban would only apply to Muslims and that Christian refugees from these affected countries would be given priority, there have been several reports of Christian refugees being turned back from the airports.