An afternoon meeting of the President's top national security advisers ended without a decision on an attack, said Ms Sarah Huckabee Sanders, the White House press secretary.
Defence Department officials noted it may be difficult to extricate the Trump administration from a strike, given the President's Twitter post a day earlier that US missiles "will be coming, nice and new and 'smart'".
"We are continuing to assess intelligence and are engaged in conversations with our partners and allies," Ms Sanders said in a statement.
She said Mr Trump would be speaking later on Thursday with Prime Minister Theresa May of Britain and President Emmanuel Macron of France, the two main partners expected to join military action.
Defence officials said General Mattis was urging caution and consideration of a wider strategy - including trying to get more commitments from allies of immediate help after any strikes against President Bashar al-Assad in Syria.
He also underscored the importance of a preponderance of evidence linking Mr Assad to Saturday's suspected chemical weapons attack on a suburb of Damascus, the capital, the officials said.
The Trump administration has not yet confirmed the use of chemical weapons by the Syrian regime.
Earlier on Thursday, Mr Trump said he would make a decision "fairly soon" about a strike. In a tweet, he insisted that he had never telegraphed the timing of an attack on Syria, which "could be very soon or not so soon at all!"
Mr Macron cited unspecified proof that the Syrian government had used chemical weapons in a deadly attack on Douma, outside of Damascus.
He said that France was working in close coordination with the Trump administration on the issue.
In London, the British Cabinet agreed "on the need to take action to alleviate humanitarian distress and to deter the further use of chemical weapons by the Assad regime", and that Prime Minister Theresa May "should continue to work with allies in the United States and France to coordinate an international response", the statement said.
British submarines were ordered within missile range of Syria, according to The Daily Telegraph.
NY Times
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