
Zaghari-Ratcliffe, 37, has been detained since early April and is accused by Iran's Revolutionary Guards of trying to overthrow the Iranian government.
Theresa May's inbox: Uniting kingdom and country, uncoupling from EU
"The Prime Minister raised concerns about a number of consular cases involving dual nationals, including that of Mrs Zaghari-Ratcliffe, and stressed the importance of resolving these cases as we worked to strengthen our diplomatic relationship," May's office said after the two leaders spoke on the telephone.
Zaghari-Ratcliffe works for the Thomson Reuters Foundation, a London-based charity that is independent of Thomson Reuters and operates independently of Reuters News.
May and Rouhani also spoke about the implementation of the deal made between Iran and foreign powers about its nuclear program, with May saying Britain would make efforts to enhance banking cooperation with Iran.
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