This shows Tehran is regaining market share at a faster pace than analysts had projected as it battles with Saudi Arabia for customers by cutting its prices. April loadings at 2.3 million barrels per day (bpd) were around 15 percent higher than the International Energy Agency estimated earlier this month.
May shipments are set to jump to 2.1 million bpd from 1.3 million bpd during the same month in 2015, when Iranian exports were constrained by Western sanctions imposed because of the country's nuclear programme. The April loadings were the highest since January 2012.
The increase in loadings suggests that Iran has overcome a tanker shortage that threatened to derail attempts to regain market share after the sanctions were lifted in January.
Saudi Arabia will feel the surge in Iranian exports most keenly as it struggles for regional supremacy with Iran, with the oil market becoming a key battleground.
Saudi Arabia plans to boost production in the coming months to squeeze the Iranians, said Ian Bremmer, the president of political risk consultancy Eurasia Group, who spoke recently with executives and a member of the ruling family.
The production increase could also boost returns for the planned Saudi Aramco share sale and help ensure a smooth succession for deputy crown prince Mohammed bin Salman, Bremmer told Reuters on Wednesday.
Increases of as much as 1 million bpd were mentioned, Bremmer said, though he was sceptical about the higher targets.
"The challenge against Iran will mean an expanded effort to work with Asian economies," he said.
That will mean investing in refineries in the Asian market, "something the Iranians can't do, given both their resource limitations and the remaining sanctions environment," he said.
In the meantime, Iranian exports are rapidly returning to near pre-sanctions levels. Loadings to Asia were 1.7 million bpd in April, about a third higher than a year ago and the most since 2011, according to the source.
Loadings will stay near that level for May, with 1.6 million bpd scheduled.
Loadings for China, Iran's biggest customer, were nearly 840,000 bpd in April and more than 620,000 bpd are planned for May.
Iran's sales to Europe, including Turkey, are also rising fast, according to the source. April loadings to Europe totalled 487,000 bpd and are set for 400,000 bpd this month. European countries were buying as much as 800,000 bpd before 2012.
Oil major Total SA is set to take 160,000 bpd of crude in May, down from the 240,000 bpd loaded in April. The company, along with Spain's Cepsa, signed import deals with state-owned National Iranian Oil Co soon after the sanctions were lifted in January.
Loadings to Spain are set for 32,000 bpd in May, while Greece will take 65,000 bpd.