Saudi Arabia has agreed to a limited cease-fire in several areas of Yemen including the capital Sana’a, which is controlled by Iranian-backed Houthi rebels, as part of broader efforts to end a four-year conflict that has threatened to escalate into regional war.

A Yemeni government official and a diplomat said attempts were underway to expand the truce. Saudi officials couldn’t immediately be reached for comment.

Last week, the Houthis announced a unilateral halt to the hundreds of drone and missile attacks that have targeted OPEC’s largest producer in recent years.

The apparent breakthroughs follow a devastating attack on major Saudi oil facilities that briefly halved the country’s output and rattled global markets this month. Yemen’s Houthis said they carried out the attack using a swarm of unmanned aircraft, but the U.S. has said Iran was responsible.

Oil fell after Friday’s news, first reported by Dow Jones, that a partial Yemen cease-fire was in place. Crude had already been heading for a weekly decline as Saudi Arabia is about a week ahead of its repair schedule following the attack on Abqaiq and a nearby oil field, and is pumping more than 8 million barrels a day, according to people familiar with the matter.

Yemen has been on the front lines of a broader standoff between Iran and Saudi Arabia for years and United Nations efforts to broker a lasting truce have repeatedly struggled to gain traction as regional powers continued to support opposing sides. But the scale of the Abqaiq attack, which took out 5 per cent of global supply, exposed the vulnerability of a sector vital to the global economy and has given new impetus to diplomatic efforts.

Mohammed Ali Al-Houthi, a member of the ruling Political Council, rejected the move as insufficient, according to the rebels’ Al-Masirah TV, and said the group would accept nothing short of “a comprehensive stop to the aggression and the lifting of the blockade” on the Red Sea port of Hodeida in return for the cease-fire it announced last week.

A Yemeni diplomat who has links to different parties of the conflict said there are serious ongoing discussions about the duration and scope of the cease-fire and whether it will cover all territories or just the capital. The discussions are being mediated by Western countries, he said, adding this might be a first step toward either a total cease-fire or a complete halt to airstrikes by the Saudi-led coalition.

The United Arab Emirates and Saudi Arabia entered Yemen’s civil war in 2015 to support the government of President Abd Rabbuh Mansur Hadi after the Houthis managed to seize control of Sana’a and other cities. Despite the overwhelming military superiority of the Gulf allies, the war has turned into a quagmire that has crept ever closer to home.

Recognizing the growing danger of a regional escalation, the U.A.E. has signaled that it intends to scale back its presence, with the last soldier leaving by year-end.

The Saudi cease-fire comes on the heels of a visit to the country earlier this month by U.S. Assistant Secretary of State for Near Eastern Affairs David Schenker, who said Washington was talking with the Houthis. The Wall Street Journal was the first to report that the Trump administration was also trying to cajole Saudi Arabia into negotiations with rebel leaders, at a time when concerns over a possible broader conflict with Iran were growing.