Iran seized the British-flagged Stena Impero, which has 23 crew members of Indian, Russian, Latvian and Filipino nationalities aboard on Friday, media reports said.
Stena Bulk, the shipping company that owns the vessel, said in a statement that the tanker was "approached by unidentified small crafts and a helicopter during transit of the Strait of Hormuz while the vessel was in international waters. We are presently unable to contact the vessel which is now heading north towards Iran".
Iran's Revolutionary Guard forces, in a statement on their website, said the ship was seized for "non-compliance with international maritime laws and regulations" and was being brought to an unnamed Iranian port.
The vessel sailing to Saudi Arabia was seen changing its course and heading north towards the Iranian island of Qeshm, marine tracking data showed.
Stena Bulk said "there have been no reported injuries and their safety is of primary concern to both owners and managers".
Later, Iran's Islamic Revolutionary Guard Corps also seized a Liberian-flagged tanker Mesdar. The tanker's owner later said the ship was briefly boarded by armed guards before being allowed to go. Iran's semi-official Fars news agency tweeted that the Mesdar had left Iran's territorial waters.
The Iranian private Tasnim news agency said that the British-owned Mesdar was cleared to continue its course, after having received a warning from the authorities over safety and environmental issues.
Britain and Iran have been locked in a bitter row ever since a super tanker Grace 1 carrying Iranian crude oil was seized by the British marines in the Strait of Gibraltar on suspicion of violating European Union (EU) sanctions against Syria.
Tehran denied the accusations and also accused the UK of acting on behest of the US.
British Foreign Secretary Jeremy Hunt has termed the seizure of the oil tankers as "unacceptable".
"It is essential that freedom of navigation is maintained and that all ships can move safely and freely in the region," he said.
"We're not looking at military options, we're looking at a diplomatic way to resolve the situation, but we are very clear that it must be resolved," Hunt later told Sky News, warning that if the situation is not resolved quickly "there will be serious consequences".
President Trump on Friday said that Iran is "nothing but trouble" and that "we heard one, we heard two" tankers were seized.
"Iran is showing their colours," Trump told reporters. "Iran is in big trouble right now. Their economy is crashing, it's coming to a crash... It's very easy to straighten out or it's very easy for us to make it worse."
Late Friday, US Central Command (CENTCOM) said the US had intensified air patrols over the Strait of Hormuz. CENTCOM spokesman Lt. Col. Earl Brown said that US Naval Forces Central Command had been "in contact with US ships operating in the area to ensure their safety".
( With inputs from IANS )