Mattis, however, said the assault was a "one-time shot", so long as Assad does not repeat his use of chemical weapons.
To Trump, the move was emblematic of Obama's weakness.
One area Mr Ciobo would draw the line on the United States entry is over its previous demand for pharmaceutical patent protections.
Several huge explosions were heard in Syria's capital early Saturday, AFP's correspondent there said, as US President Donald Trump announced strikes on the country were under way.
The president's dilemma is that strength and resolve do not necessarily equal a well-thought out Syria strategy. The planes fired Storm Shadow missiles at a facility where the United Kingdom said the Assad "regime is assessed to keep chemical weapon precursors stockpiled".
American officials doubted that Russian Federation or Iran would counterattack directly against USA forces in the region. Or he can do nothing and risk appearing weak.
Australian Prime Minister Malcolm Turnbull, commenting after Trump's tweet, said it would be "great" to have the United States back in the pact though doubted it would happen.
Even as he promised to strike again if Assad used chemical weapons, Trump made clear that he had no interest in staying in Syria.
On Monday, he said he would "be making some major decisions over the next 24 to 48 hours".
Trump has signaled in recent weeks that, despite advice from his national security team, he wanted to accelerate the timetable of the withdrawal of American forces.
Three confirmed targets were struck: a scientific research centre near Damascus, a chemical weapons storage facility west of Homs and a chemical weapons facility serving as a command post.
Tottenham vs Manchester City, Premier League
The latter won't happen and City will likely be crowned champions on April 22 or 29. "The players have my total respect". City go into this off the back of three consecutive defeats and appearing vulnerable for the first time under Guardiola.
The U.S. and Russian Federation have both supported local allies against the Islamic State militant group (ISIS), but disagree over Syria's political future, a dispute that now threatens to take a violent turn. "No amount of American blood can produce lasting people in the Middle East - the fate of the region lies in the hands of its own people". "It is a troubled place", he said.
"There is an open door for the United States to rethink and take advantage of the window of opportunity", Enrique Pena Nieto suggested in Lima.
Russian officials and President Trump have exchanged heated rhetoric since Trump began talk of a US response to the alleged chemical attack throughout the past week.
The limited strikes were deplored by the Syrian opposition, which saw the West as lacking an worldwide strategy for dealing with the civil war. Trump, by contrast, did not mention diplomacy in his remarks. He said the three nations have "marshaled their righteous power".
"His dream would be to have a strong military that protects our homeland", said the administration official.
US defense and military officials told CNN that aircraft, including B-1 bombers, and at least one US Navy warship based in the Red Sea, participated in the strikes.
Trump has said he will hold the Syrian government, as well as its Russian and Iranian allies, accountable for the suspected attack. "That's all he cares about". From a distance, USA missiles hitting suburbs of the capital sounded like thunder.
By Thursday, Trump made the final decision to authorize the strike. But the damage was limited, and a defiant Assad returned to episodic use of chlorine and perhaps other chemicals.
Russia, too, was hardly caught off guard. "But sooner or later it fails and fails catastrophically".
Haley blasted Russia for protecting Syria and said Moscow has emboldened the Syrian regime to continue its attacks, while the Russian ambassador to the United Nations said Washington had embarked on an "illegal military adventure".
"Could not have had a better result", he tweeted.