The Saudi government has agreed to a partial ceasefire in Yemen in response to the Houthis' announcement a few days ago to halt attacks on the kingdom.
Although the Houthis fired two missiles at Saudi Arabia this week, leaders in Riyadh saw the attack as not dangerous to undermine new ceasefire efforts, the Wall Street Journal reported.
Riyadh has agreed to a limited ceasefire in four areas, including the Yemeni capital Sanaa, which has been controlled by the Houthis since 2014.
If successful, the Saudis would seek to extend the truce to other parts of Yemen.
Bloomberg also quoted sources as saying that Saudi Arabia was moving towards a partial ceasefire in Yemen.
The sources said the Saudi decision followed a surprise move by the Houthi group, which announced a unilateral ceasefire in Yemen last week.
The Houthi group's move came just days after it claimed responsibility for the September 4 attack on Saudi Aramco oil facilities.
Saudi Arabia and Washington blame Iran for the attack, saying the Houthis have neither the weapons nor the skills to carry out this sophisticated attack.