The meeting marks a rare diplomatic engagement between senior officials from Washington and TehranThe first round of high-level US-Iran talks in Switzerland was suspended after about 80 minutes on Sunday, with Iran's delegation reportedly leaving the venue in protest over US President Donald Trump's threat to "hit Iran very hard again" if Tehran failed to rein in its proxies in Lebanon.The meeting marked a rare diplomatic engagement between senior officials from Washington and Tehran as efforts intensify to ease tensions across West Asia and address longstanding disputes. US vice president JD Vance met Iranian representatives in talks facilitated by Pakistan and Qatar, with both sides seeking to explore a broader path towards de-escalation.According to officials familiar with the discussions, the agenda includes Iran's nuclear programme, the future of the fragile interim understanding between the two countries and unresolved issues surrounding the Strait of Hormuz.During the talks, Vance conveyed President Donald Trump's message that Washington was prepared to significantly improve ties with Tehran if progress could be achieved through diplomacy.Highlighting the significance of the engagement, Vance said, "Never before has the Iranian and American leadership met at such a high level. We've already made great progress over just the last few hours, and I expect that we will make additional progress in the hours to come."At the same time, he cautioned against expecting a quick breakthrough, stressing that meaningful diplomatic agreements require compromise and sustained effort."Peace is never easy. Peace always requires a little bit of work. It always requires a little bit of give and take," Vance said.While negotiators continued discussions behind closed doors, President Trump issued a fresh warning to Tehran over the activities of Iranian-backed groups in Lebanon.Posting on his Truth Social platform, Trump called on Iran to immediately restrain its allies in Lebanon and warned of a strong American response if violence continued.The statement represented one of Washington's toughest messages since the launch of the latest diplomatic initiative in Switzerland."Iran must immediately stop their highly paid PROXIES in Lebanon from causing trouble. If they don't, we'll hit Iran very hard again, just like we did last week, only harder!!!" Trump posted.The warning came as diplomats sought to keep negotiations on track despite growing tensions linked to the conflict in Lebanon and broader regional security concerns.