Riyadh led a military coalition into Yemen in 2015 to prop up the government, but it has struggled to oust the war-torn country's highly motivated guerrilla opponents.
Yemen's Houthi rebels have said that their attacks against Saudi Arabia and loyalist forces would cease if the Riyadh-led military coalition supporting the Yemeni government stopped its raids.
"I am directing a message to the new American administration and to the Saudis: stop your attacks and we will stop ours against you. It's as simple as that," said Hisham Sharaf, foreign minister in the Houthi administration, which is not internationally recognised.
Sharaf made the comments during a news conference in Sanaa on recent armed drones headed for Saudi Arabia and fighting between the rebels and government forces in the Marib region.
The coalition said Sunday and Monday that it had intercepted two drones heading for the kingdom.
Sharaf said rebels had acted against "extremist groups" in the Marib area that had come to bolster groups supporting President Abedrabbo Mansour Hadi.
The region, east of the rebel-held capital, is the government's last northern stronghold.
Saudi air power intervened against the rebels and the Houthis were "obliged to respond", Sharaf said.
Yemen has been locked in conflict since the rebels took control of the capital Sanaa in 2014 and went on to seize much of the north.
Riyadh led a military coalition into Yemen in 2015 to prop up the government, but it has struggled to oust its highly motivated guerrilla opponents.
Saudi Arabia has repeatedly accused regional rival Iran of supplying sophisticated weapons to the Houthis, a charge Tehran denies.
The US has said it is "deeply troubled by continued Houthi attacks".
"We call on the Houthis to immediately cease attacks impacting civilian areas inside Saudi Arabia and to halt any new military offensives inside Yemen," the State Department said in a statement Sunday.
Sharaf meanwhile denied any suggestion the rebels had carried out a deadly December attack targeting the new Yemeni government at the airport in second city Aden.
He called for a "neutral" international investigation to determine the perpetrators of the attack, which has been blamed on the Houthis.
He also warned the Houthis were "a very important part of any peace process" and could not be ignored.
Tens of thousands of people, mostly civilians, have been killed and millions displaced in Yemen's war, which the United Nations has called the world's worst humanitarian disaster.