One of the ships reportedly struck a mine, causing a fire on board, the Revolutionary Guard said in a statement.
It is not clear what caused the fire on board the other ship, but the Revolutionary Guard said it “encountered an incident” while being escorted by US military personnel.
There is no information on the extent of the fires.
Iran has severely restricted traffic through the strait since the war with the US and Israel broke out in February. The US has responded with a blockade of Iranian ports.
Iran has recently claimed several times that oil tankers have struck mines in the strait.
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