"The United States military, with our interagency team, is working with our partners to address this unprecedented attack and defend the international rules-based order that is being undermined by Iran," he said in a tweet.
Esper said he and the Pentagon leadership met with Trump in the wake of Saturday's attack, which analysts say appear to have involved drones and possibly cruise missiles launched from a nearby country.
Earlier he also spoke with Saudi Crown Prince Mohammad bin Salman as well as Iraqi Defense Minister Najah al-Shemmari.
There was, however, no suggestion of what kind of response Washington or its Gulf allies were considering.
The Iran-supported Huthi rebels in Yemen claimed responsibility for the attack.
But the Riyadh-led coalition fighting the Huthis said earlier Monday that the weapons were Iranian-made, and it remains unclear where they were launched from.