Mattis held talks with Defence Minister Avigdor Lieberman on Friday morning, to be followed by meetings with Prime Minister Benjamin Netanyahu and 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 President Donald Trump pledging unstinting support for the country.
Despite tensions over Israeli settlement building, 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 hopes 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. Trump has denounced Iran's "harmful influence" in the Middle East.
Israel is closely watching Iran's presence in neighbouring Syria, where it is backing President Bashar al-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.
"By establishing itself permanently in Syria with the support of Hezbollah, Iran wants to create a territorial axis linking its territory to Lebanon through Iraq and Syria, which could only endanger the security of Israel," Israeli Intelligence Minister Yisrael Katz said recently.
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.
Last month, in the most serious incident between the two countries since the Syria conflict began, Israeli warplanes struck several targets there, drawing retaliatory missile fire.
Israel used its Arrow interceptor to destroy what was believed to have been a Russian-made SA-5 missile, and Lieberman threatened to destroy Syria's air defence systems "without the slightest hesitation" if it happened again.
Israel was also among the first countries to salute Trump for a recent US strike on a Syrian airbase over an alleged chemical attack on a rebel-held town.
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 in the region.
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.
In a further sign of close relations, Israel is to receive three more F-35 stealth fighter jets on Sunday, adding to two which arrived in December.
They are among 50 that Israel has agreed to buy from US aerospace giant Lockheed Martin..
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