Speaking at a White House press conference with Lebanon's Prime Minister Saad Hariri, Trump also called the Lebanese Shiite militia Hezbollah a threat to the entire Middle East.
Trump pledged continued US military aid to Lebanon following his Oval Office meeting with Hariri.
"I'm not a fan of Assad. I certainly think that what he's done to that country and to humanity is horrible," Trump said.
Recalling that he had ordered cruise missile strikes on Assad for using chemical weapons, Trump said: "I am not somebody that will stand by and let him get away with what he tried to do."
Trump also claimed Syria would be different today had his predecessor Barack Obama taken action against Assad after drawing a "red line in the sand" over his regime's use of chemical weapons.
"Had president Obama gone across that line and done what he should have done, I don't believe you'd have Russia, and I don't believe you'd have Iran, anywhere near the extent and maybe not at all, in Syria today," he said.
Trump accused Iran and Hezbollah, which the United States considers a "foreign terrorist organization," of fueling the humanitarian disaster in Syria.
"Hezbollah is a menace to the Lebanese state, the Lebanese people and the entire region," he said.
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"The group continues to increase its military arsenal which threatens to start yet another conflict with Israel," Trump said. "With the support of Iran, the organization is also fueling humanitarian catastrophe in Syria."
Hezbollah's "true interests are those of itself and its sponsor, Iran," he added.
Trump demurred when asked to comment on possible additional sanctions against Hezbollah.
"I'll be making my position very clear over the next 24 hours," he said. "I have meetings with some of my very expert military representatives and others, so I'll be making that decision very shortly."
Trump praised the Lebanese army for "fighting continually to guard Lebanon's border and prevent ISIS (the Islamic State group) and other terrorists... from gaining a foothold inside their country.
"The United States military has been proud to help in that fight and will continue to do so," he said. "America's assistance can help ensure that the Lebanese army is the only defender Lebanon needs."
Later at an embassy reception, Hariri underscored that point: "We would like to see the armed forces take control of all territory of Lebanon."
The current draft State Department budget calls for cuts in US military assistance and analysts say Lebanon could be among the countries affected.