LOWER MACUNGIE TOWNSHIP, ⁠Pennsylvania/DUBAI - U .S. President Donald Trump said on Tuesday that Iran had agreed to nuclear inspections into "infinity," while Tehran said it had made no such concession in negotiations, raising questions about the ‌viability of their fragile peace deal.

The two countries, which ended a first round of negotiations in Switzerland 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 their framework deal signed last week aiming to end the war.

Nevertheless, Trump said negotiations with Iran were going smoothly. "We're getting along quite well," he said at a rally in Pennsylvania.

The United States also relaxed travel curbs on Iran's World Cup ​soccer ​team, allowing it to travel from Tijuana, Mexico, to Seattle two days before its next match instead of one.

In signs of withering domestic support for the war, Trump's poll numbers weakened while the Republican-controlled Senate defied the president and voted to halt the war, in a largely symbolic move that highlighted fissures in his party.

A Reuters/Ipsos poll found 35% of Americans think the U.S. is now ⁠in a weaker position with Iran than before the war, while 23% believe it is in a stronger position.

The Senate vote of 50-48 endorsed a resolution passed by the House of Representatives this month, reflecting growing concern even among some of Trump's Republicans about the unpopular conflict that began on February 28.

It was the first time both chambers of Congress had passed a resolution directing a president to remove U.S. armed forces from hostilities under the War Powers Act, though it was not immediately clear how the votes might affect the conflict.

RESCUING SEAFARERS

Though prospects for a lasting peace are far from certain, the initial agreement between Washington and Tehran has allowed traffic ​to flow again through the strait, which ‌typically handles one-fifth of global ⁠energy supply.

Trump said on Wednesday he ⁠had told the Justice Department to look into oil companies for not lowering pump prices in line with falling crude costs.

"Gasoline prices better start going down a lot faster than what I'm seeing!" he said on social media.

Oil prices ​fell more than 1% on Wednesday, extending this week's losses and trading near their lowest since before the war began on February 28.

The United Nations' shipping agency ‌said 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, though it has said it might impose tolls or other fees on shipping subsequently.

In a joint statement on Tuesday, Iran and Oman, which controls the other side of the strait, stressed their "sovereign rights" in the waterway, adding that they would work together to manage traffic, along with associated costs.

Oman said it had coordinated with the International Maritime Organization to provide a temporary corridor for vessels seeking to transit the Strait of Hormuz.

U.S. 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 U.S. sanctions on Tehran and unfreezing Iranian assets held abroad. It also outlines a $300-billion investment fund for the Islamic Republic's reconstruction.

AT ODDS OVER NUCLEAR INSPECTIONS, FROZEN ASSETS

The framework itself sets no limits on Iran's nuclear program, an issue 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 U.S., while Iran's ambassador to the United Nations in Geneva, Ali Bahreini, said Iran would decide how to spend that money.

Washington has already agreed to waive sanctions on Iran for 60 days, allowing Tehran 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 act to "neutralize" threats against Israeli soldiers and citizens.

Even as Israel and Lebanon renewed talks in Washington on Tuesday, Israeli gunfire killed two people in ⁠southern Lebanon, its civil defence and health ministry said, prompting Iran-backed Hezbollah to accuse Israel ​of violating a ceasefire that has largely held since Sunday.

(Reporting by Reuters bureaus; Writing by Lincoln Feast, Sharon Singleton and Clarence Fernandez; Editing by Gareth Jones, Cynthia Osterman and Raju Gopalakrishnan)