Mattis made the comments during a one-day visit for talks with Israeli leaders, who strongly supported a recent US strike against a Syrian airbase in retaliation for an alleged chemical attack on a rebel-held town.
"The bottom line is there can be no doubt in the international community's mind that Syria has retained chemical weapons in violation of its agreement and its statement that it had removed them all," Mattis said during a press conference with Israeli counterpart Avigdor Lieberman.
"It's a violation of the United Nations Security Council resolutions, and it's going to have to be taken up diplomatically, and they'd be ill-advised to try to use any again. We've made that very clear with our strike."
Mattis added that Syria had "dispersed their aircraft in recent days."
An Israeli military assessment has found that Assad's regime was still in possession of "a few tonnes" of chemical weapons, an army official confirmed.
Some Israeli media reports put the number at between one and three tonnes. Lieberman declined to comment on the assessment at Friday's press conference in Tel Aviv.
Assad, backed by his ally Russia, has strongly denied the allegation that his forces used chemical weapons against the rebel-held town of Khan Sheikhun on April 4, describing it as a "100 percent fabrication".
He has said repeatedly that his forces turned over all chemical weapons stockpiles in 2013, under a deal brokered by Russia to avoid threatened US military action.
The agreement was later enshrined in a UN Security Council resolution.
Talks with Netanyahu
Mattis, the first member of President Donald Trump's cabinet to visit Israel, later held talks with Prime Minister Benjamin Netanyahu in Jerusalem, followed by President Reuven Rivlin.
Israel and the United States have long had close strategic ties, with Washington providing Israel more than $3 billion per year in defence aid and Trump pledging unstinting support for the country.
Despite tensions over Israeli settlement building, Barack Obama's administration signed a new agreement with Israel before he left office increasing the amount to $3.8 billion for a 10-year period beginning in 2018.
Mattis sought to hear directly from Israeli leaders on their concerns and what they expect from the Trump administration, a US defence official said.
Iran's influence is at the top of the list for Israel, a worry shared by the United States.
Netanyahu welcomed Mattis's comments on Iran and Syria, calling the Trump administration's approach a "welcome change."
"We sense a great change in the direction of American policy," he said.
Israel is closely watching Iran's presence in Syria, where it is backing Assad.
Israeli enemy Hezbollah is also fighting with Assad in Syria. Israel fought a devastating war against the Iran-backed Lebanese Shiite movement in 2006.
Israel has sought to avoid being dragged into the six-year civil war in Syria, but acknowledges carrying out air strikes there to stop what it says are deliveries of advanced weapons to Hezbollah.
Iran nuclear deal
Testy relations between Obama and Netanyahu reached a low point over a 2015 nuclear deal between Iran and world powers, led by Washington.
Obama pushed hard for the agreement, but Netanyahu fiercely opposed it, arguing it will not prevent Iran from obtaining nuclear weapons and that the lifting of sanctions would allow it to support proxy groups.
Trump also harshly criticised the deal, and on Thursday said Iran was "not living up to the spirit" of the agreement, adding that the United States would set out its position on it soon.
On Tuesday, Trump ordered a review of the deal to be led by his National Security Council, although the State Department admits Iran has so far stuck to its side of the bargain.
Mattis said on Friday that Iran appeared to be living up to the agreement, but that it "in no way mitigates against or excuses the other activities of Iran in the region."
Mattis's visit was part of a trip to the Middle East and Djibouti. He had previous stops in Saudi Arabia and Egypt, and will head to Qatar next.
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