Trump said the U.S. "could have gone bigger" in terms of its military response but "thought this would be the appropriate first shot."
Though the U.S. secretary of state is visiting Russia, relations have become strained over Moscow and Washington's actions in Syria.
The U.S. Secretary of State faces a tough negotiation in his Moscow visit after accusations of Russian complicity in Syrian chemical attacks.
Turkey, Saudi Arabia, the United Arab Emirates, Jordan and Qatar are to present a united front against Assad.
Sadr, who has a huge following in Baghdad, is the first Shiite leader to call for Assad to give up power in Damascus.
McMaster said the missile strike against Syria was to meant to send a "strong political message to Assad," saying the White House was "prepared to do more."
Syria's president may see the Tomahawk attack as a 'slap on the wrist' in the absence of a major strategic shift.
Secretary of State says Moscow failed to live up to a chemical weapons agreement.
Moscow had its S-400 missile system in range of the strike.
While Trump stopped short of calling on Assad to leave office, the comments were his strongest suggestion yet that the United States may be edging toward a stronger stance against Assad.
"American policy is based on creating chaos in different parts of the world and creating conflicts among states. This is not new," Syria's President Bashar al-Assad said.
Russia suggested President Donald Trump had no clear strategy in Syria after the U.S. leader said an apparent chemical attack changed his views on Syrian President Bashar al-Assad.
Secretary of State Rex Tillerson and U.S. Ambassador to the U.N. Nikki Haley said the U.S. was no longer interested in pursuing regime change in Syria.