Earlier this week, Trump called the chemical attack in Douma "atrocious" and vowed that those responsible would "pay a price".
He highlighted his country's continued determination to fight terrorists across Syria.
The fact-finding mission from the Organization for the Prohibition of Chemical Weapons was expected to head to Douma, where the suspected attack took place and where Russian Federation said rebels had now capitulated to government control.
The bombing represents a major escalation in the West's confrontation with Assad's superpower ally Russian Federation, but is unlikely to alter the course of a multi-sided war which has killed at least half a million people in the past seven years.
Russian Federation is one of Assad's strongest allies and has military bases in Syria.
"A short time ago, I ordered the United States Armed Forces to launch precision strikes on targets associated with the chemical weapons capabilities of Syrian dictator Bashar al-Assad".
His views were bolstered by Bolton and USA envoy to the United Nations Nikki Haley, who argued that any action must go well past the limited set of strikes Trump ordered from Mar-a-Lago last April, a senior administration official said.
"The Syrian Arab Republic condemns in the strongest terms the brutal American-British-French aggression against Syria, which constitutes a flagrant violation of worldwide law", the foreign ministry said.
Soldiers threw up two fingers to flash the victory sign near a auto with pictures showing the president, his late father Hafez al-Assad and ally Hassan Nasrallah, who heads the Iran-backed Lebanese Shiite movement Hezbollah.
"America's war against Syria, and against the region's peoples and resistance movement, will not achieve its aims", the group said in a statement published on its War Media Channel.
Iranian Supreme Leader Ayatollah Ali Khamenei called the strikes "crimes" in a speech cited by Iranian TV, according to Reuters. "The American president, the French president, and the British prime minister are criminals".
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Pentagon officials briefed reporters on the aftermath.
People in Damascus were awakened by the sounds of loud explosions and saw red dots flying into the sky, in what later turned out to be the air defenses responding to the missile attack. The gas attack, as claimed by him killed at least 40 people.
Both the Syrian government and Russian Federation, which backs Assad, have denied such a chemical attack took place.
Syria has denied carrying out the Douma attack and its ally, Russia, had warned that Western military strikes would risk starting a war.
The Organisation for the Prohibition of Chemical Weapons has been "working in close collaboration" with United Nations security experts "to assess the situation and ensure the safety of the team", it said.
Rafah al-Okda, a 21-year-old nursing student at Damascus University, said she had not changed her routine following the threats.
Russia's Foreign Ministry condemned the attack calling it a flagrant violation of global law. The U.K. Defense Ministry said the strikes were "successful".
Global desk - The United States and its allies United Kingdom and France have carried out bomb attacks in Syria targeting multiple government establishments where chemical weapons facilities were allegedly developed.
It said three civilians were wounded in the Homs attacks but did not give a toll for Damascus or mention any combatant casualties.
Several missiles hit a research center in Barzeh, north of Damascus, "destroying a building that included scientific labs and a training center", SANA reported.
Just after the barrage of strikes began, Syria announced it was activating its air defence system to block the attack.