The US and Saudi Arabia say they have agreed to end US refueling of Saudi aircraft bombing Yemen but several officials underlined that American training and military assistance will continue.
Riyadh has also faced criticism for the murder of Jamal Khashoggi at the Saudi consulate in Istanbul.
Norway said Friday it was freezing all defence material export licences to Saudi Arabia over recent developments in the country and the war in Yemen.
"We feel that the current situation above all else warrants a resolution that gives both the special envoy and OCHA the support they need to take a step towards ending the conflict in Yemen and the suffering of the Yemeni people", the trio said in an email to the council seen by AFP.
The refueling decision, which was first reported by The Washington Post, has been under discussion for a few weeks.
Mattis acknowledged "continued bipartisan interest from Congress", and said the Trump administration is "appreciative of the continued dialogue we have had with key members on this issue".
Since the outbreak of the invasion in 2015, the United States military has been refueling Saudi aircraft that conduct airstikes on Yemen. United States officials, who spoke on condition of anonymity to discuss internal deliberations, said Senate staffers were asked about the issue Thursday and whether their bosses would support it.More news: NASCAR Might Take Away Wins If Teams Keep Cheating Next Season
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Anti-war groups hailed the decision as a victory and called for the U.S. to go further in halting support for the campaign.
"I'm glad that the Trump administration is ending USA refueling of Saudi aircraft in Yemen's devastating war..." USA officials told Reuters only a fifth of Saudi-led coalition aircraft require in-air refueling from the United States.
Mattis said the United States would play a continuing role to help the Saudi-led coalition and Yemeni forces minimize civilian casualties and expand humanitarian efforts.
The coalition reiterated its hope that the UN-sponsored negotiations with the Houthi rebels in a third country, touted as Sweden, will "lead to a negotiated settlement" and "end the aggression" of the militias that overran major population centres in Yemen from 2015 onwards. It said that the coalition, which relies heavily on air power, has killed scores of civilians in recent airstrikes, and rebels are responding with mortars in residential neighborhoods that cause indiscriminate casualties.
Earlier this year, Mattis had defended USA military support to Saudi-led coalition forces in Yemen, when lawmakers weighed forcing the Pentagon to end Washington's involvement.
The US has provided the Saudis and their UAE coalition partners with intelligence, aerial refueling and military advice, but US forces are not directly involved in the airstrikes or other aspects of the fighting.
The war has plunged Yemen into an increasingly dire humanitarian situation and the threat of starvation is widespread.
The conflict in Yemen, the Arab world's poorest country and home to an estimated 28 million people, began with the Houthis takeover of Sanaa and toppling of Hadi's government. Human rights groups say the real death toll may be five times higher.