in briefTrump claims Iran has agreed to inspections on its nuclear facilities, Iran says that's not the case. The US has eased travel restrictions on Iran's FIFA World Cup team, in a sign of easing tensions.US President Donald Trump said on Tuesday that Iran had agreed to nuclear inspections into "infinity," while Iran said it had made no such concession in negotiations, raising questions about the viability of their fragile peace deal.The two countries, which held a first round of negotiations in Switzerland that ended on Monday, also offered conflicting accounts about financial incentives for Iran, control of the Strait of Hormuz, and Israel's parallel war in Lebanon — all major aspects of the framework deal they signed last week that aims to end the war.Nevertheless, Trump said negotiations were going smoothly with Iran. "We're getting along quite well," he said at a rally in Pennsylvania.In a sign of easing tensions, the US relaxed travel restrictions on Iran's World Cup soccer team, allowing the squad to travel from Tijuana, Mexico, to Seattle two days before its next match instead of one.A Reuters/Ipsos poll found 35 per cent of Americans think the US is now in a weaker position with Iran than it was before the war, while 23 per cent believe it is in a stronger position.News that makes senseYour trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.The Republican-controlled Senate, meanwhile, defied Trump and voted to halt the war, in a largely symbolic move that highlighted fissures in his party.Rescuing seafarersThough prospects for a lasting peace are far from certain, the initial agreement has allowed traffic to flow again through the strait, which typically handles one-fifth of global energy supply.Oil prices on Tuesday were at their lowest level since before the war began on February 28, and the United Nations' shipping agency said a it was working to evacuate 11,000 seafarers stranded when Iran closed the strategic waterway.The agreement calls for Iran to allow traffic to flow freely for 60 days, but Iran has said it might impose tolls or other fees on shipping after that point.Iran and Oman, which controls the other side of the strait, issued a joint statement on Tuesday stressing their "sovereign rights" in the waterway and saying they would work together to manage traffic, along with associated costs.US secretary of state Marco Rubio, visiting Gulf allies unsettled by the peace deal, said Iran would not be allowed to charge tolls in the strait as part of any final agreement.The deal calls for an immediate end to the war, including in Lebanon, lifting US sanctions on Iran and unfreezing Iranian assets held abroad. It also outlines a US$300 billion ($428 billion) investment fund for the Islamic Republic's reconstruction.At odds over nuclear inspections, frozen assetsThe framework itself imposes no limits on Iran's nuclear program, a subject to be tackled in 60 days of negotiations.Trump claimed that Iran had agreed to allow international inspectors indefinite access to its damaged nuclear sites."Iran has fully and completely agreed to highest level Nuclear inspections long into the future (Infinity!!!)," Trump said on social media.Iran denied it had discussed its nuclear program at the talks and said it had not agreed to invite International Atomic Energy Agency inspectors back to the country.The two sides also disagreed on details of a provision that would give Iran access to funds that have been frozen in overseas accounts.Trump said any unfrozen assets would be used to buy food and medical supplies from the US, while Iran's ambassador to the United Nations in Geneva, Ali Bahreini, said Iran would decide how to spend that money.The US has already agreed to waive sanctions on Iran for 60 days, allowing Iran to sell oil and related products and receive payment for them.Israel's parallel war against Iran-backed Hezbollah in Lebanon also remains a sticking point. Bahreini said the deal requires Israel to withdraw its troops from Lebanon, while Israel has said it will maintain a security zone in southern Lebanon and continue to act to "neutralise" threats against Israeli soldiers and citizens.State media in Lebanon said Israeli gunfire had killed two people there on Tuesday, and Hezbollah said the incident violated the ceasefire.For the latest from SBS News, download our app and subscribe to our newsletter.