Global oil prices have tumbled and stock markets rallied amid fresh hopes that a US-Iran peace deal may end the greatest energy supply crisis in the history of the market.

The price of Brent crude dropped 4% to below $84 (£62) a barrel as the new trading week began in financial centres across Asia-Pacific, amid optimism that the strait of Hormuz could reopen shortly and bring a return of Gulf oil exports to the market.

Trump said on Sunday that a deal was “now complete”, despite recent Israeli airstrikes on Beirut that had threatened to undermine the sensitive talks.

The US president wrote on social media: “I hereby fully authorize the toll free opening of the Strait of Hormuz, and, simultaneously herewith, authorize the immediate removal of the United States Naval blockade. Ships of the World, start your engines. Let the oil flow!”

An hour later he clarified that the strait would open after the peace deal was signed on Friday and that “for purposes of mine removal, oil will flow on both ends again for the Region, and the World!”

Many of the details of the agreement are unclear, notably around the exact timing of the reopening of the maritime route, who will oversee safe passage and whether any conditions will be applied. Iranian authorities have said there would be a 60-day negotiating period for a final deal tackling wider issues such as Tehran’s nuclear programme and sanctions relief.

The benchmark international oil price extended the falls recorded on Friday to just over $83 a barrel, its lowest since the early days of the war, on 10 March. Brent crude was just below $73 at the outbreak of the war in late February.

The oil price began tumbling late last week from $93 a barrel on Thursday to close at $87.50 on Friday after Trump said he was close to reaching a peace deal with Tehran that would end the regime’s effective chokehold on the oil trade route.

Global stock markets rallied on Monday. In Europe, the UK’s FTSE 100 rose by 0.8%, while the French Cac 40 and the German Dax were both up 1.8%. Shares in oil companies, including BP and Shell, fell in early trading.

In Asia, a region heavily dependent on oil imports, Japan’s Nikkei index and South Korea’s Kospi jumped by 5%, while China’s CSI300 index rose by 1.9%.

The US president also claimed that the US military had been secretly helping to move millions of barrels of oil a day through the strait in recent weeks to help ease the pressure in the global market.

Oil prices have remained lower than expected throughout the Iran war which brought Gulf oil exports through the strait to a halt in early March, effectively erasing 20m barrels of oil a day from the market – or a fifth of the market’s supplies.

Gulf producers have managed to reroute about 5m barrels of oil a day to the market via pipelines to alternative regional export hubs, while in recent weeks a further 2m barrels a day could have found their way to the market with the help of the US military via “dark tankers” that shuttle cargoes undetected to vessels waiting in the Gulf of Oman before returning to reload.

However, there are still a number of ships suck in the strait of Hormuz. The Japanese Shipowners’ Association said on Monday that there were still 38 Japanese-linked vessels stranded in the channel.

A spokesperson for the body said that it wanted to “wait a little longer for more concrete information” about the US-Iran peace deal, which is expected by 19 June when the pact is due to be signed in Switzerland.

Elsewhere, a record level of emergency crude and fuel has been released into the market by members of the International Energy Agency at a rate of about 2.5m barrels a day.

The world’s oil supply shortfall has also been narrowed by cuts to demand: China is estimated to have cut its imports by about 4m barrels a day to reach lows not experienced in a decade, potentially by drawing on its record high inventories to meet demand and halting its aggressive stockpiling of recent years.

Globally, demand may have fallen by between 3m and 4m barrels of oil a day as petrochemical refineries across Asia have cut back their activity to weather the crisis.

Tony Sycamore, an analyst at IG, said on Monday that countries would use a reopening to replenish depleted stockpiles and refill strategic reserves.

He said negotiations were complex, particularly around nuclear issues, and that it was therefore “hard to see crude falling much further from here in the near term”.