The US secretary of state, Marco Rubio, has said no country, including Iran, would be allowed to charge tolls for shipping in the strait of Hormuz as he sought to reassure US allies in the Gulf that Washington would take a firm line in peace negotiations with Tehran.

Rubio is to meet Gulf allies on Tuesday and Wednesday in an attempt to reassure them that the US remains committed to their security and the 60-day ceasefire deal struck with Iran last week will not embolden Tehran.

Arriving in Abu Dhabi on Tuesday, Rubio said the US would provide for freedom of navigation through the strait of Hormuz and that no country would be allowed to charge a toll there, which Iran has said it has a right to do.

“It’s an international waterway,” Rubio said. “No country is allowed to charge tolls or fees on an international waterway. That’s existing international law. That’s the way it is in international waterways all over the world, and that’s the way we expect it’ll be here.”

That was just one of a number of potential fault lines in the shaky new US ceasefire deal, as concerns have grown that the release of Iran’s frozen assets would be reinvested into its military. And while Donald Trump claimed on Monday that Iran had agreed to allow international inspectors back into the country to monitor its nuclear programme, Iran directly denied that an agreement had been struck.

Rubio also nodded to the potential spoiler role that Israel’s conflict with Hezbollah in Lebanon could play in the agreement, saying that Iranian proxies must also respect the ceasefire but that the issue would be addressed “at the appropriate time in these negotiations”.

The US last week signed a ceasefire agreement with Iran that established a 60-day period of toll-free passage through the strait, after which Iran and Oman would discuss the “future administration and maritime services in the strait of Hormuz, in discussions with other Persian Gulf littoral states, in line with applicable international law and the sovereign rights of coastal states of the strait of Hormuz”.

Observers took that to mean that Iran was not directly precluded from charging fees or services for transport through the strait of Hormuz. Rubio, however, indicated that he believed Iran would accept the terms of toll-free passage through the waterway.

“I don’t think we have anybody to convince around here in that regard,” he said on Monday. “I think all the countries in this region would agree with us.”

The Gulf is divided over the deal. While Qatar has played a central role in mediating the agreement, some countries – notably the United Arab Emirates, Kuwait and Bahrain – are fearful it hands Iran substantial sums that may be ploughed into its military.

The mood among Gulf states remains one of anger with Iran. The US allies want absolute clarity that tolls will not be charged in the strait of Hormuz, and also want any final agreement to also address limits on Iran’s ballistic missiles programme. Iran’s president, Masoud Pezeshkian, said on Tuesday that Iran’s ballistic missiles programme would “never” be part of a future agreement. “If we did not have our missiles, which are for our self-defence, Israel and America would have ploughed through Iran the way they did Gaza,” he said.

Donald Trump said in a post to his Truth Social platform on Tuesday that the unfrozen assets would be under US control and used to buy food and medical supplies from the US.

In his first trip to the region since the US and Israel started the war on 28 February, Rubio will visit the UAE, Kuwait and Bahrain, the state department said. He is also likely to meet officials from the Gulf Cooperation Council regional body.

All three countries, which house large US military bases, have been hit by Iranian missiles, but the US has declined to detail the scale of the impacts. Severe penalties have been imposed on those using social media to reveal the damage.

Trump last week disclosed that the UAE played an active part in mounting counterattacks against Iran, and the Iranian foreign ministry spokesperson, Esmail Baghaei, said Iran believed the UAE, Kuwait and Jordan all helped the US attack Iran.

“We will definitely not abandon this issue. We will both document and demand,” Baghaei said. “The US military presence in the region has shown what consequences and harm it has brought to the region and its countries. We hope that the countries of the region have learned from the experience of the past few months and years.”

The long-term Iranian aim is to persuade the Gulf states to eject the US from the region. In what is still a fluid debate inside Iran and the Gulf, some Iranian voices are calling for a rapprochement with the region, perhaps by forming an alliance with a powerful new grouping of Turkey, Saudi Arabia, Pakistan and Egypt. The Iranian president, Masoud Pezeshkian, flew to Pakistan on Tuesday in his first overseas visit since the war ended.

There have also been signs that the UAE – the Gulf state with the closest economic ties with Iran – is also looking to defuse the crisis in relations with Iran.

In the short term, Iran is expecting roughly $6bn (£4.54bn) of its assets locked in Qatar due to US sanctions to be unfrozen, with another $6bn to be given by Doha as a repayable loan.

Over the next two months Iran can also expect to receive at least $8bn of income since the US Treasury’s decision on Monday to issue a sanctions waiver on Iranian oil exports. The treasury’s waiver document details that the payments can be made in dollars.

Some internal Iranian estimates claim the income from unhindered oil sales – principally to China – could rise to more than $30bn over a year. Iran has long been evading US sanctions by covertly trading with China but at heavily discounted prices.

The shipping monitors Kepler said 36 ships passed through the strait of Hormuz on Monday, the highest traffic volume since 1 March. Iran’s chief negotiator, Mohammad Bagher Ghalibaf, has said he was working with Oman on a long-term agreement to manage the strait. Ghalibaf met the Sultan of Oman on Monday in Muscat.

Tehran and Washington had clashed on Monday over whether – as Trump and the US vice-president, JD Vance, have claimed – unfrozen Iranian assets could only be used to buy US agricultural produce such as soya beans. Iran’s central bank governor, Abdolnaser Hemmati, said the memorandum of understanding did not obligate Iran to spend unfrozen assets on US goods, and purchase decisions would be made on the basis of quality and price.

Iran also disputed claims that Rafael Grossi, the director general of the UN nuclear inspectorate, had been given an Iranian green light to prepare to return to Iran to inspect the damaged nuclear sites.

Iran also said further work was needed on the establishment of a mechanism to monitor the proposed Lebanon ceasefire. The MOU states that the US, Iran and “their allies in the current war” declare the “immediate and permanent termination of military operations on all fronts, including in Lebanon” – a formulation that clearly gives the impression of trying to bind Israel to an end to operations against Hezbollah.

This could complicate the US-backed Israel-Lebanon ceasefire reached in early June, which stated that any cessation of hostilities must be agreed directly between Israel and Lebanon, and not through a separate track.