In a statement, they said: "We would like to take this opportunity to address the distressing situation concerning Craig and Lindsay Foreman who are currently being detained in Kerman, Iran.
A Foreign Office spokesperson earlier said: "We are providing consular assistance to two British nationals detained in Iran and are in contact with the local authorities.".
A British couple who have been detained in Iran have been named by their family as Craig and Lindsay Foreman.
Iranian state media said on Wednesday that a man and woman were in custody in Iran's southeastern city of Kerman on security-related charges.
This unexpected turn of events has caused significant concern for our entire family, and we are deeply focused on ensuring their safety and well-being during this trying time.