In a separate statement, U.S. Secretary of State Rex Tillerson said there was "no doubt" forces loyal to Syrian President Bashar Assad were behind the attack, which killed at least 70 civilians, and added that he sees no role for Assad in Syria's future.
"There is no doubt in our minds, and the information we have supports that Syria, the Syria regime under the leadership of President Bashar al-Assad, are responsible for this attack," Tillerson told reporters.
Trump stopped short of calling for Assad's removal on Thursday, but told reporters traveling with him on Air Force One, "I think what Assad did is terrible."
"I think what happened in Syria is a disgrace to humanity and he's there, and I guess he's running things, so something should happen," he added.
The Pentagon and the White House are discussing a range of military options that could be pursued in response to the attack, according to Reuters.
Asked whether the U.S. would lead international efforts to remove the Syrian president, Tillerson replied that "steps are underway," Peter Baker of The New York Times reported.
Tillerson also urged Syria's ally Russia to reconsider its stance on Assad.
"It is very important that the Russian government consider carefully their continued support for the Assad regime," he said.
Those comments represent a stark turnaround from a statement Tillerson made last week on a trip to Turkey. Signaling that Assad's removal from power was not a priority, the secretary of state said the "longer-term status of President Assad will be decided by the Syrian people."
This is a developing story and will be updated.