In one of her final important acts as prime minister before resigning on Wednesday, May will chair a meeting of Britain's COBR emergencies committee at around 10:30 am (0930 GMT), her Downing Street office said.
"As well as receiving the latest updates from ministers and officials, the COBR meeting will discuss the maintenance of the security of shipping in the Persian Gulf," a spokeswoman said in a brief statement.
It will be Britain's third emergency committee meeting since Iran seized the Stena Impero tanker on Friday, in what London has told the UN Security Council was an illegal move conducted in Omani waters.
The meeting will be the first May has chaired on the seizure.
Cabinet Office Briefing Rooms (COBR) meetings typically bring together ministers, security, intelligence and military chiefs in a secure facility in central London.
Britain has a frigate, the HMS Montrose, in the Gulf, and has requested all British-flagged ships to avoid the Strait of Hormuz chokepoint until further notice.
Meanwhile, British Foreign Secretary Jeremy Hunt spoke to his French and German counterparts over the issue, his office said.
"Both ministers agreed with the foreign secretary that safe passage for vessels through the Strait of Hormuz is a top priority for European nations, while avoiding any possible escalation," it said in a statement.
"They agreed to keep in close contact and to work together to achieve this," the statement said.
Letter to UNSC
In its letter to the UN Security Council, Britain said that Iran had claimed that the Swedish-owned Stena Impero had tried to enter the strait through the exit route, while not responding to messages or warnings and with its transponder switched off.
"This is not the case," the letter said.
Iranian officials have also claimed that the tanker was detained due to a collision with an Iranian fishing boat, the letter said, adding: "There is no evidence of this.
"Even if it had occurred, the ship's location within Omani territorial waters means that Iran would not have been permitted to intercept the Stena Impero."
Junior defence minister Tobias Ellwood said Sunday that Britain was considering several options.
Asked if Britain could introduce new sanctions or freeze Iranian assets, finance minister Philip Hammond told BBC television: "We've already got a wide raft of sanctions against Iran, particularly financial sanctions, so it's not clear that there are immediate things we can do but we are of course looking at all the options."
Foreign Secretary Jeremy Hunt has said parliament will be updated on the situation on Monday.
Either Hunt or former London mayor Boris Johnson will be confirmed as the new leader of the governing Conservative Party on Tuesday and take over from May as prime minister on Wednesday.
It will be Britain's third emergency committee meeting since Iran seized the Stena Impero tanker on Friday