"We are considering an appropriate response (to the) violations of all previous UN resolutions, violations of international norms," he said in televised comments at the Palm Beach International Airport in Florida, where he greeted Chinese President Xi Jinping who was arriving for a summit with US President Donald Trump.
Tillerson did not specify what actions the United States would take.
According to CNN, two US Navy warships armed with tomahawk cruise missiles -- the USS Ross and the USS Porter -- are stationed in the Mediterranean.
Trump has said that "something should happen" in Syria.
Spicer said every country's number one priority is toprotect its own people.
"We've got to do what we can to make sure that, as we seek to root out ISIS and terrorism throughout the world, that we don't at the same time do things that would bring those same threats to our country," he said.
"You've seen the president talk to several folks in the region about the setting up of safe zones and the supporting of them. Our hearts break for the people of Syria who were innocently attacked the other day, especially these young children who we watched," he said.
Joining the chorus, top Republican Senator John McCain said that Assad must go.
"We agree with the President that Assad has crossed a line with his latest use of chemical weapons.
The message from the United States must be that this will not stand.
We must show that no foreign power can or will protect Assad now.
He must pay a punitive cost for this horrific attack," he said in a statement.
"If the President is willing to take the necessary action, he deserves broad bipartisan support, and we will help build it," said McCain, who is Chairman of the Senate Armed Services Committee.
The former Secretary of State, Hillary Clinton, too called for removal of Assad.
"I wish, obviously I wish that the international community writ large had been able to rein this in," she said.
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