Talks in Switzerland between the US and Iran were still ongoing despite Iranian media reports that negotiators had left the venue, according to people familiar with the matter.Two semi-official Iran media outlets said Tehran had halted talks with the US after President Donald Trump threatened fresh strikes over the actions of Hezbollah in Lebanon. But negotiators remained engaged in Switzerland, said the people, who were granted anonymity to describe sensitive matters.Also read: Iran halts Switzerland talks after Trump threatens fresh strikesAs the meetings got under way earlier Sunday, Trump said in a social media post that he would strike Iran again if it doesn’t “immediately stop their highly paid PROXIES in Lebanon from causing trouble.”He also warned Iran that the US might start collecting tolls if there’s no deal. Speaking Sunday to Fox News, he said he told Iranian leaders directly that if they close Hormuz, “You won’t even make it back” to Iran, using an expletive.The first high-level meetings of US, Iranian, Qatari and Pakistani representatives had commenced Sunday in the Swiss resort of Bürgenstock, with US Vice President JD Vance and Iranian Foreign Minister Abbas Araghchi among attendees.A resolution to the fighting in Lebanon will be decisive for the success of the US-Iran talks in Switzerland, according to an official familiar with the discussions, who asked not to be identified discussing sensitive information.The conflict emerged as a key roadblock, with other issues in focus being the Strait of Hormuz, US sanctions and frozen Iranian assets, the person said. Four-party talks started at 2:45 p.m. local time and were supposed to continue Sunday evening. The Swiss are keeping the venue ready until mid-morning on Monday, allowing negotiations to run until then if necessary.Also read: Trump warns Iran: Stop Lebanon proxies or face ‘harder’ US strikesIsrael, Washington’s partner in the war on Iran that began Feb. 28, has been fighting a parallel campaign against Hezbollah in neighboring Lebanon. Iran has consistently sought to link the conflict there, which has killed thousands and displaced more than 1 million Lebanese, with the broader US negotiations.Israel has insisted it’ll keep troops on its borders until it’s sure that Hezbollah, designated a terrorist organization by the US, is no longer a threat. The Israel Defense Forces said its recent operations are targeting a network of underground bunkers where Hezbollah fighters are believed to be sheltering.