A week after Yemen’s Iran-backed Houthi rebels expanded their control along the Red Sea coast, the conflict is raising a bigger question: could their gains give Iran another lever over Saudi Arabia and global oil markets? The Houthis have pushed towards a key maritime chokepoint, attacked Saudi-linked shipping and targeted oil facilities, while also appearing to eye Yemen’s oil-rich east. The developments have already pushed up global fuel prices and added fresh pressure on Saudi Arabia, the world’s largest oil exporter. The international terror group advance has also opened another potential pressure point for Iran as the United States works to loosen Tehran’s grip on the Strait of Hormuz, on the other side of the Arabian Peninsula. The Houthis captured the Red Sea port city of Mokha and several islands near the Bab el-Mandeb strait, a narrow waterway through which around 12% of global trade passes in peacetime. They are also fighting around Marib, a city in an oil-rich province that serves as a military hub for Saudi-backed forces. The Houthis also threaten Taiz, another major front in Yemen’s long-running civil war. The latest offensive has forced an estimated 125,000 Yemenis to flee their homes. Yemen’s 12-year civil war has killed more than 150,000 people and repeatedly pushed the country towards famine. The Houthis have also been firing at Saudi oil facilities and tankers. An attack on Saudi Arabia’s East-West pipeline, blamed on Iran-backed militias in Iraq, has added to concerns over the kingdom’s oil exports and rattled global markets. The Houthis say their demand is for Saudi Arabia to lift its long-running blockade on territory under their control. "It is Saudi Arabia that closed the Bab el-Mandeb strait to shipping traffic to and from Yemen and imposed an unjust blockade on the country," Mohammed al-Bukhaiti, a member of the Houthi political bureau, told The Associated Press. The Houthi gains could give Iran another potential source of leverage in the wider regional conflict, particularly as pressure around the Strait of Hormuz remains a major concern. The Houthis have said they are targeting Saudi shipping, but analysts warn their definition of Saudi-linked vessels could expand. "At the moment, their focus is on Saudi-linked shipping," said Valentin d'Hauthuille, a Middle East analyst at ACLED, a conflict monitor. But they might "extend the criteria according to which vessels are assessed to be 'Saudi-linked' to increase pressure on both Saudi and the global economy." For now, shipping traffic through the Bab el-Mandeb has recovered. Windward, a shipping firm, recorded a fall from 35 daily transits before the Houthi advance to 25 afterwards, but traffic later rose to 45 transits on Sunday. That recovery could offer some relief to global markets, but the Houthis could still expand their targets beyond Saudi ships and tankers. Saudi Arabia and its allies have struggled for years to contain the Houthis. The latest offensive could force Riyadh to consider diplomatic options, while the United States appears reluctant to get directly involved.