Israel has not confirmed launching the attack, which reportedly killed 14 people, including seven Iranians.
Trump is considering his military options in Syria after Saturday's alleged chemical attack against the rebel-held town of Douma. The Syrian government has denied the allegations.
The President also insisted that the US would not remain engaged in Syria forever under any circumstances. The U.S. military fired 59 Tomahawk cruise missiles from the Mediterranean Sea, but the strike had little effect as the air base was up and running in just 24 hours.
Mattis said Friday there were no reports of U.S. losses in what he described as a heavy but carefully limited assault.
"Our decision will not target allies of the regime or attack anyone but rather attack the regime's chemical capabilities", he said, insisting he did "not want an escalation".
As fears of a Russia-West military confrontation mounted, French President Emmanuel Macron expressed his "deep concerns" over the situation in Syria in a phone call with Russian President Vladimir Putin.
"Never said when an attack on Syria would take place", Trump tweeted early Thursday.
German Chancellor Angela Merkel is less conflicted: she's ruled out joining any military action against Syria. "On a strategic level, it's how do we keep this from escalating out of control, if you get my drift on that", he said.
Citing information previously released by local health organisations, WHO said that "an estimated 500 patients presented to health facilities exhibiting signs and symptoms consistent with exposure to toxic chemicals".
Hundreds of Russian contractors and mercenaries are reported to be working in Syria.
After the Douma attack, the insurgent group dug in there - Jaish al-Islam - finally agreed to withdraw. But the description from an ally put things differently.
"We're maintaining that we have a number of options and all those options are still on the table".
The White House said Wednesday that Trump "holds Syria and Russia responsible for this chemical weapons attack". He added that the use of nuclear weapons is "unlikely".
Tonight, Russia's Ambassador to the UN, Vassily Nebenzia, urged the US and allies to show restraint and said the "immediate priority is to avert the danger of war". "But our efforts have been repeatedly thwarted" by Syria and Russia, she said.
One way to ensure Al Assad cannot use such weapons is to conduct strikes on his chemical infrastructure, including by targeting factories and weapons holding areas. "It does not exist anymore".
France already has some 1,100 troops involved in its Operation Chammal, created in 2014 to fight Islamic State extremists in Iraq and extended in 2015 to Syria, as part of the U.S. -led coalition. Residents of Damascus came there to rally and march, away from the heavy security in the capital.
Trump did not detail what a strike on Syria would look like, or whether these would be US missiles.
In 2017, Trump launched a cruise missile strike against a Syrian air base in retaliation for a sarin attack the UN later pinned on Assad.
Russian officials alleged quickly after last Saturday's suspected attack that the images of victims in Douma were fake.
Decisions will be made "fairly soon", President Trump said. They are in eastern Syria, far from Damascus.