U.S. forces helping to evacuate Afghans desperate to flee Taliban rule were on alert for more attacks on Friday (August 27).
Two blasts and gunfire rocked the area outside the airport on Thursday evening, witnesses said.
Islamic State (ISIS), an enemy of the Islamist Taliban as well as the West, said one of its suicide bombers targeted "translators and collaborators with the American army".
It was not clear if suicide bombers detonated both blasts or if one was a planted bomb.
It was also not clear if ISIS gunmen were involved in the attack or if the firing that followed the blasts was Taliban guards firing into the air to control crowds.
U.S. officials vowed retribution.