Mattis's visit, his second to the region, is the latest in a string of appearances by top US officials who have scrambled to reassure partners about US commitments.
While campaigning, Trump sparked broad anxiety by calling into question long-standing security assumptions and mutual defence treaties with Japan and South Korea.
But the US leader's views have shifted since he took office, and Mattis told reporters he would be underscoring American support for the region.
"I will emphasize the United States stands with our Asia-Pacific allies and partners," Mattis told reporters traveling with him, "reinforcing the international order necessary to secure a peaceful, prosperous and free Asia with respect for all nations upholding international law."
Mattis will deliver his message at a policy speech at the Shangri-La Dialogue on Saturday.
The summits have in recent years been dominated by concerns over China's rapid build up of islets and maritime features in the South China Sea, where Beijing has reclaimed thousands of acres of land and installed military fortifications.
The issue remains front and center, but this year the focus is also on North Korea and its accelerating push to develop an intercontinental ballistic missile.
Pyongyang on Monday test-fired another rocket, the latest in a series of launches and atomic tests that have ratcheted up tensions over its quest to develop weapons capable of hitting the US -- something Trump has said "won't happen".
Since taking office, Trump, who laced his campaign rhetoric with anti-China sentiment, has made an about-face and turned to China to apply pressure on North Korea to rein in its nuclear weapons program.
After meeting with President Xi Jinping in April, Trump, who once accused China of "raping" the US, praised its leader as a "good man", saying it would be inappropriate to pressure Beijing while Washington is seeking its help with Pyongyang.
The posture shifts have left some in the region seeking clarity on US policy.
"There's concern over China's rise and it's assertive behaviour, particularly in maritime space," said David Helvey, a top Pentagon advisor for Asian and Pacific security affairs.
"And there's also questions about where the United States is going to be in the Asia-Pacific region in the new administration."
Freedom of navigation
Mattis's challenge is to reassure allies that America can apply pressure on China over the South China Sea, while at the same time convincing Beijing that controlling North Korea is in its own security interests.
Underscoring the point, the US Navy on May 25 conducted a "freedom of navigation" operation in the South China Sea, when the USS Dewey guided-missile destroyer sailed within 12 nautical miles of Mischief Reef in the Spratly Islands.
It was the first such procedure since October, leading some to speculate America was going easy on China to secure concessions on North Korea.
But Helvey insisted US views have not shifted.
"We remain concerned about any effort to further militarize those islands," he said.
"We would oppose any action that would impinge upon the fundamental principle of freedom of navigation."
While such sailings in the South China Sea have in recent years been conducted only sporadically, albeit with great fanfare, the Pentagon wants to ramp up the pace so they become viewed as routine.
North Korea meanwhile has carried out two atomic tests and dozens of missile launches since the beginning of last year.
The US military last week successfully tested a ground-based missile defense system that for the first time intercepted a dummy intercontinental ballistic missile, destroying it in space.
"The Department of Defence is focused on strengthening alliances, empowering countries to be able to sustain their own security, and strengthening US military capabilities to deter war," Mattis said.
In another signal to Pyongyang, the United States is currently conducting joint operations with two aircraft carrier strike groups and the Japanese navy in the Sea of Japan.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)