Houthi rebels say they have successfully targeted a British and a US ship in the Red Sea, casting doubt on the effectiveness of three waves of US-UK strikes on missile sites belonging to the group in Yemen. Neither of the two ships were badly damaged but the incident will underscore the need for commercial ships either to pay higher insurance premiums or take longer, more expensive routes to avoid the threat of Houthi attacks. A third ship was targeted on Tuesday afternoon, but not struck, at least reassuring Britain that the Houthi capabilities may have been degraded by the US-UK airstrikes. The US envoy for Yemen, Tim Lenderking, said the US was trying to provide the Houthis with a way to climb down, adding that the Houthi attacks were doing the opposite of helping the Palestinians. He said the peace road map prepared by Saudi Arabia was frozen as a result of the Houthi strikes, adding: “That plan had a lot of goodies for the Houthis” that they should not throw away. He warned that “the longer this drags out, the more this tempts miscreants within Yemen to take matters into their own hands”, a reference to the possibility that forces aligned to the UN-recognised government in Aden would seek to relaunch their war against the Houthis. “We need to hear more Yemini voices saying what the Houthis are doing is not good for Yemen and not a way to show solidarity with Palestinians. It is driving donors away from Yemen,” he said. Lenderking, who is due to visit the region next week, accused Iran of fanning the conflict. Speaking to the Middle East Institute, he said: “The sense we have is overwhelmingly that Iran is pushing on an open door here with the Houthis. Aiding, abetting, sharing intelligence, helping them target ships, and determining which are the more lucrative targets.” But the Houthi leader, Abdul-Malik al-Houthi, said in a televised speech that the group would “seek to escalate more and more if the barbaric and brutal aggression against Gaza does not stop”. A Houthi spokesperson, Yahya Saree, explaining the latest attacks, said in a statement on Tuesday: “We carried out two military operations, the first targeted an American ship (Star Nasia), and the other targeted a British ship (Morning Tide).” The Greek-owned Star Nasia, managed by Star Bulk Carrier, was damaged by an explosion at 11.15am GMT, a Greek shipping ministry official said, adding that its crew members were not injured. It is unclear whether the explosion was caused by a sea mine or a rocket, the official added. The security company Ambrey reported earlier on Tuesday that a British ship flying the Barbados flag “suffered minor damage to its port” 57 nautical miles from the coast of Hodeidah, without any casualties. The ship continued on its way. The United Kingdom Maritime Trade Operations agency said just after midnight on Tuesday that it had received a report of a projectile fired at the port side of a ship west of Hodeidah and that a small craft was seen nearby. The projectile passed over the deck and caused slight damage to the bridge windows, but the vessel and crew were safe and proceeded on the planned passage, it added. On Monday the UK defence secretary, Grant Shapps, told MPs there had been a change in the cadence of Houthi strikes. “The clock is running down for the Houthis, in as much as their ability is being degraded,” he said. “They do not have the eyes and ears from the radar stations; they are more reliant still on Iran.” Meanwhile, the government in Aden has sacked its prime minister, replacing him with the hardline anti-Houthi foreign minister, Ahmed Awad bin Mubarak. Hugely experienced, Mubarak is sceptical of plans by Saudi Arabia to strike a peace deal with the Houthis to formally bring Yemen’s civil war to a close. Last Thursday he said Iran’s al-Quds force operatives had been deployed to Yemen’s coastline. The reshuffle will reflect concerns in the US about the quality of the anti-Houthi alliance in the country. The prime minister is overseen by a disparate eight-strong presidential leadership council, some of whom are backed by Saudi Arabia and others by the United Arab Emirates.