Iranian President Mohammad Khatami and Tony Blair would like to meet, Mo Mowlam has revealed in Tehran.
Ms Mowlam delivered a message from Mr Blair to Mr Khatami and said Britain was interested in promoting ties with Iran, the Islamic Republic News Agency reported.
It did not provide details on the message's contents.
Ms Mowlam is the first British cabinet minister to visit Iran since the 1979 Islamic revolution.
"I think they are keen to meet each other but it is pending because of elections in both countries," Ms Mowlam said after talks with President Mohammad Khatami.
Iran will hold presidential elections on June 8 and the general election in Britain is widely expected in May.
Britain and Iran exchanged ambassadors in May 1999 after a 20-year break. Relations have improved since the 1997 election of Khatami, who has sought closer links with the West.
Ms Mowlam signed a memorandum of understanding with Iran on tackling the problems of drug trafficking and addiction.
She also toured a rehabilitation centre in Isfahan and pledged support for Iran's fight against drug trafficking. Iran has often complained of a lack of adequate Western support for its fight against drug trafficking.
Iran is a major route for smuggling drugs from Afghanistan and Pakistan to the western markets.