Washington provides intelligence as well as aerial refuelling to coalition warplanes conducting air strikes in Yemen.
The United States provides limited military support to a Saudi-led coalition which for two years has been fighting in support of Yemen's government against rebels supported by Iran.
On Wednesday, Mattis will meet the kingdom's top leaders in Riyadh.
Washington provides intelligence as well as aerial refuelling to coalition warplanes conducting air strikes in Yemen with American-supplied weapons.
Rights groups have repeatedly criticised the coalition bombing campaign in Yemen for causing civilian casualties.
Asked by reporters about the chance of stepping up American support, Mattis did not reply and instead put the accent on a return to peace talks.
"Our aim is that this crisis can be handed to a team of negotiators under the aegis of the United Nations that can try to find a political solution as quickly as possible," he said as he flew to Riyadh.
Seven ceasefires alongside peace efforts by the United Nations have so far failed to stop the fighting.
It is necessary to end the "firing of missiles provided by Iran against Saudi Arabia" as well as "the death of innocent people in Yemen", Mattis said.
Yemen's Huthi rebels allied with troops loyal to ex-president Ali Abdullah Saleh have fired ballistic missiles into Saudi Arabia.
Rebels have also shot short-range rockets over the kingdom's southern border, killing least 130 soldiers and civilians.
Washington alleges that Iran, Saudi Arabia's regional rival, has shipped missiles to Yemen but Tehran denies the charge.
A United Nations Panel of Experts in January reported that it "has not seen sufficient evidence to confirm any direct large-scale supply of arms" from Iran.
Some in US President Donald Trump's administration would like to increase American military support for the Saudi-led coalition to better counter Iranian ambitions in the region.
Sunni-dominated Saudi Arabia regularly accuses the Shiite-majority Islamic republic of interference in the Middle East, and Mattis has called Iran the world's "biggest state sponsor of terrorism".
The UN estimates that more than 7,700 people have been killed over the past two years and more than 40,000 wounded in impoverished Yemen, which faces a serious risk of famine.
Riyadh has expressed optimism that Trump's team will be more engaged in the region, particularly in containing Iran, compared with former president Barack Obama.
In December, the Obama administration blocked a sale of precision guided weapons to Saudi Arabia because of concerns over civilian casualties in Yemen.