The statement did not name British-Iranian mother, Nazanin Zaghari-Ratcliffe, who has been detained since April 2016, but her case is likely to be a key focus of his trip.
In his most serious misstep as Foreign Secretary, Johnson was forced to apologize last month after his comments about Zaghari-Ratcliffe raised fears that her jail sentence could be prolonged.
Johnson told a parliamentary committee that Zaghari-Ratcliffe had been teaching journalism during her visit to Iran, but he later clarified that she had been visiting relatives before she was detained.
The comments appeared to lead to Zaghari-Ratcliffe being summoned to an unscheduled court hearing, at which Johnson's remarks were cited as proof that she had engaged in "propaganda against the regime."
Zaghari-Ratcliffe has been in jail since she was detained at Tehran airport in April 2016. There have been concerns that Johnson's remarks may lead to an extension to her five-year sentence.
The Foreign Secretary later backtracked.
"Of course I apologize for the distress, for the suffering that has been caused by the impression that I gave that the government believed, that I believed, that she was there in a professional capacity. I do apologize," Johnson said.
The apology did not spare Johnson from biting criticism, with many opposition politicians calling for him to be sacked.
Johnson's successor as the mayor of London, Sadiq Khan, told the BBC that if Prime Minister Theresa May was a strong leader, "she would have sacked him a long time ago."
The trip will be the first for a British Foreign Secretary to Iran since 2015 and only the third since 2003, according to the Foreign Office.
Johnson is set to arrive in Oman Friday, before traveling to Iran Saturday and the United Arab Emirates Sunday.
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