The US has sent an aircraft carrier and extra troops to the Middle East in recent weeks to deter Iranian aggression.
These blasts come a month after four oil tankers were damaged in an unclaimed attack off the United Arab Emirates.
In particular, Khamenei said the USA has shown itself not to be trustworthy or genuine in its peace talks offer by continuing to ramp up economic sanctions on his government, including sanctioning Iran's petrochemical industry last Friday.
Earlier the incident was discussed at a meeting of the United Nations, which warned the world can not afford "a major confrontation in the Gulf" as global concern grew over suspected attacks on commercial ships near the Strait of Hormuz.
Already, Iran says it quadrupled its production of low-enriched uranium.
Pompeo, in turn, said it was the Supreme Leader that had "rejected Prime Minister Abe's diplomacy today by saying he has no response to President Trump and will not answer".
The US military released a video it said shows Iran's Revolutionary Guards removing an unexploded limpet mine from one of the oil tankers targeted near the Strait of Hormuz, suggesting the Islamic republic sought to cover up evidence of its involvement from the scene.
Safe havens including Gold are on the bids as a recent tussle between the USA and Iran over 2 oil tankers' blast in the Gulf of Oman turns serious.
A Revolutionary Guard patrol boat pulled alongside the ship and removed the mine, Central Command spokesman Capt. Bill Urban said.
Tehran has denied responsibility for the 12 May attacks.
Iranian Foreign Minister Mohammad Javad Zarif has described the incidents as suspicious.
Pompeo did not take questions after giving the brief statement. One of the officials claimed a USA military aircraft recorded the footage.
"There are lots of moving parts and "facts" at the moment, so my only advice would be treat things with extra caution", said one security official, who spoke on condition of anonymity.
United Nations secretary-general Antonio Guterres strongly condemned the attacks, warning that the world can not afford "a major confrontation in the Gulf region".
An Iranian navy boat tries to stop the fire of an oil tanker after it was attacked in the Gulf of Oman, June 13, 2019.
Explosions also struck the Japanese-owned Kokuka Courageous, which was loaded down with methanol, but the fire on board was soon extinguished. Twenty-one mariners from one of the ships were taken aboard a U.S. Navy destroyer after having abandoned ship, while 23 mariners from the other vessel were reportedly taken to Iran.
The attack on the tankers that were carrying "Japan-related" cargo notably came during a rare visit to Tehran by Japanese Prime Minister Shinzo Abe.
The Kokuka Courageous is now sailing toward the port of Khor Fakkan in the United Arab Emirates, with the crew having returned to the ship after evacuating because of the incident, Kokuka President Yutaka Katada told a press conference.
"This would seem very clumsy timing from a country (Iran) seeing the first tangible signs of any easing of the crippling sanctions imposed by the Americans", Bloomberg columnist Julian Lee wrote in an op-ed.
Tensions between Iran and the United States, along with its allies including Saudi Arabia, have risen since U.S. President Donald Trump pulled out of a deal a year ago between Iran and global powers that aimed to curb Tehran's nuclear ambitions in exchange for sanctions relief. "Whoever is behind the attacks is no friend of Iran".
In May, President Donald Trump tightened United States sanctions on Iran - mainly targeting its oil sector. After meeting Rouhani on Wednesday, Abe warned of unintended clashes in the Middle East. He also tied Iran to a drone attack by Yemen's Iranian-backed Houthi rebels on a crucial Saudi oil pipeline around the same time.
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