He added that he planned to speak to Iranian Foreign Minister Manouchehr Mottaki about the matter.
"We are confident that our staff have not engaged in any improper or illegal behaviour. We remain deeply concerned about the two members of our staff who remain in detention in Iran," he said in a statement.
On Wednesday, Iran's semi-official Fars News Agency said that one of those detained "had a remarkable role during the recent unrest in managing it behind the scenes."
Iranian officials deny the election was rigged, saying it was the nation's "healthiest" since the 1979 Islamic revolution.
The authorities have portrayed the unrest as the work of local subversives and foreign powers, especially Britain.
Jannati reiterated accusations by other senior Iranian figures that the West had plotted a so-called "velvet revolution" to undermine the Islamic Republic's establishment.
(Additional reporting by Luke Baker and Adrian Croft in London, David Brunnstrom in Brussels and Niklas Pollard in Stockholm; Writing by Fredrik Dahl; Editing by Richard Balmforth)