Speaking at a White House press conference, Trump said the attack had "crossed a lot of lines for me" and that it could not be tolerated.
Trump did not offer any details of how US strategy on Syria would change, and he did not directly criticize Russia, which has stood by Assad in the face of worldwide condemnation of the attack.
But Trump said details of the attack had affected him profoundly. "Yesterday's chemical attack, a chemical attack that was so horrific in Syria against innocent people, including women, small children and even beautiful little babies, their deaths were an affront to humanity," Trump said, speaking in the Rose Garden alongside Jordan's King Abdullah.
"These heinous actions by the Assad regime cannot be tolerated. The United States stands with our allies across the globe to condemn this horrific attack and all other horrific attacks, for that matter."
Earlier in the day, Trump's Secretary of State, Rex Tillerson, said there was "no doubt" that Assad was responsible for the attack on a rebel-held town in Idlib province
, northwest Syria. He called on Russia to "really think carefully" about its continued support for Assad.
Syria denied using chemical weapons and blamed rebels for the carnage. Russia, Syria's strongest ally, said it had no warplanes in the vicinity and said the deaths were the result of a regime airstrike on a chemical weapons factory on the ground controlled by "terrorists."
Asked about the first statement released by the White House after the attack on Tuesday, which blamed the attack in part on the policies of former President Barack Obama, Trump said: "I now have responsibility, and I will have that responsibility and carry it very proudly."
Trump said that Obama, who in 2012 said the use of chemical weapons by the Syrian regime would be a "red line," had missed a "great opportunity" to deal with Assad.
"It is now my responsibility. It was a great opportunity missed," Trump said.
Trump maintained that Obama's failure to enforce his red line threat "was a blank threat (that) set us back a long ways, not only in Syria but in many other parts of the world."
At a hastily convened meeting of the United Nations Security Council, the US ambassador Nikki Haley strongly condemned Russia and the Syrian government. She suggested the US was open to using military action
to end the country's ongoing civil war.
"When the United Nations consistently fails in its duty to act collectively, there are times in the life of states that we are compelled to take our own action," Haley said. "For the sake of the victims, I hope the rest of the council is finally willing to do the same."
Trump also left the door open to new action in Syria. "You will see," Trump said when asked if he would take new action, according to pool reporters present when the President welcomed King Abdullah to the Oval Office.
"These are very troubled times in the Middle East, and we see what happened just recently yesterday in Syria -- horrible. Horrible, horrible thing. Unspeakable."