(Bloomberg) — A Houthi rebel leader welcomed comments by Saudi Arabia’s crown prince on stopping the fighting in Yemen, the latest signal momentum is growing behind efforts to end a conflict that’s pushed the Gulf to the brink of war.“The optimism of Mohammed Bin Salman on stopping the war is positive,” a member of the rebels’ ruling political council, Mohammed Al-Houthi, said on Twitter. Turning the opening into meaningful negotiations requires “seriousness and dealing realistically” with the situation, he said.In a Sunday interview for CBS’s “60 Minutes,” the prince said that ending the Yemen war through a peace deal would be “much easier” if Iran stopped backing the Houthis. Still, he said, “today, we open all initiatives for a political solution in Yemen.”Saudi Arabia and the United Arab Emirates entered the Yemen war in 2015 to restore an allied government ousted by the Houthis. The conflict, which has killed thousands of people and left millions facing chronic food and water shortages, soared to the top of the world’s agenda after Sept. 14 drone and missile strikes on critical Saudi oil facilities were claimed by the Houthis.The U.S., Saudi Arabia and major European nations concluded the rebels didn’t possess the sophistication needed to launch attacks that embarrassed one of the world’s leading purchasers of American military hardware — knocking out almost 5% of global oil supply — and pointed the finger instead at Iran.After first indicating he was readying a military reprisal, President Donald Trump opted to tighten sanctions on Tehran, while the U.K., Germany and France have pushed for talks with Iranian President Hassan Rouhani.Prince Mohammed on Sunday backed that approach, warning that a war between his country and Iran would lead to a “total collapse of the global economy” and should be avoided.A “political and peaceful solution is much better than the military one,” the prince said. Iran denies it carried out the strikes, saying the Houthis were most likely responsibleThe prince said he’s in favor of Trump and Iranian President Hassan Rouhani holding face-to-face talks.End SanctionsTrump — who won the White House vowing to remove the U.S. from wars overseas and faces re-election next year — had talked up the possibility of meeting Rouhani until the attack on Saudi oil facilities.Iran has said it won’t negotiate with the U.S., a longtime foe, until it drops sanctions reimposed after Trump exited the 2015 nuclear deal last year. In response to the U.S. economic offensive, Tehran has abandoned some of its enrichment commitments under the accord.While previous cease-fires between the Houthis and the Saudi-led coalition in Yemen have collapsed, the recent violence and the risk it carries of a wider war could be catalyzing peace efforts.Saudi authorities are yet to comment on Houthi claims over the weekend that rebel fighters killed or captured hundreds of Saudi troops in raids across the border.However, a Yemeni official said Friday that Saudi Arabia had agreed to a limited cease-fire covering parts of Yemen, including the Houthi-controlled capital Sana’a, a week after the rebels announced an end to drone and rocket strikes on the kingdom.The U.A.E. has already begun to scale back its role as the war threatened to ignite a wider conflict with Iran.Calling on Saudi Arabia to end its airstrikes on Yemen, Iran on Monday said the kingdom had contacted Rouhani through a mediating country.“One of the heads of states carried a message from Saudi Arabia to Mr. Rouhani, but we need to see clear signs from the Saudis, the first of which is stopping attacks on Yemen,” Ali Rabiei, government spokesman, said in a press conference, without naming the country.To contact the reporters on this story: Mohammed Hatem in Dubai at mhatem1@bloomberg.net;Arsalan Shahla in Tehran at ashahla@bloomberg.net;Hailey Waller in New York at hwaller@bloomberg.netTo contact the editors responsible for this story: Lin Noueihed at lnoueihed@bloomberg.net, Mark WilliamsFor more articles like this, please visit us at bloomberg.com©2019 Bloomberg L.P.