Brent crude oil touched its highest since November 2014 at $77.20 a barrel. The benchmark contract was up $1.90 a barrel, or more than 2.5 percent, at $76.75 by 1335 GMT, according to a report by Reuters.
US light crude was up $1.70 a barrel, or almost 2.5 percent, at $70.76, near highs also last seen in late 2014.
In China, the biggest single buyer of Iranian oil, Shanghai crude futures hit their strongest in dollar terms since they were launched, Presstv reported.
Also on Tuesday, Trump signed a presidential memorandum to re-impose what he described as the “highest level of sanctions” against Iran.
The memorandum specifies that many of the sanctions should be re-imposed in 90 days — by August 6, 2018. The most important ones – as reported by media – would be a ban on Iran over buying or acquiring US dollars.
Another set of sanctions will once again be clamped down on Iran within the next 180 days. The most important sanctions would be those concerning Iran’s oil sales and energy sector investment as well as transactions with the Central Bank of Iran (CBI).
Analysts' estimates of the possible reduction in Iranian crude supplies as a result of any new US sanctions range from as little as 200,000 barrels per day (bpd) to as much as 1 million bpd, with most impact from 2019 as sanctions take time to be imposed.
Several refiners in Asia said on Wednesday they were seeking alternatives to Iranian supplies.
A number of countries have already cut reliance on Iranian oil, as well as other "traditional" sources of supply, due to surge in cheaper US crude exports.
Saudi Arabia said it would work with other producers to lessen the impact of any shortage in oil supplies. The country has been leading efforts since 2017 to withhold production to prop up prices, Reuters added.