She is serving a five-year jail sentence for alleged sedition, which she denies.
During a meeting with Rouhani on the sidelines of the UN General Assembly, “you can expect the prime minister to raise our ongoing consular cases, including that of Nazanin Zaghari-Ratcliffe”, a the official said.
“The prime minister will express serious concern about Nazanin’s ongoing detention and call for her to be released upon humanitarian grounds.”
On Wednesday, May will hold one-on-one talks with US President Donald Trump, focusing on her hopes of agreeing a trade deal after Britain leaves the European Union.
“They both have a strong commitment to securing a strong UK-US free trade agreement when we’ve left,” the official said.
The pair will also discuss the poisoning of a Russian double agent and his daughter earlier this year in the English city of Salisbury, which London and its allies — including Washington — blamed on Moscow.
Russia has strongly denied the accusation.