In a letter to judiciary chief Ayatollah Mahmoud Hashemi-Shahroudi, Mr Ahmadinejad described Neda's death as "suspicious," reported the official Irna news agency on Monday.
His letter added: "I request you to order the judicial system to seriously follow up the murder case... and identify elements behind the case and inform the people of the result," reported Irna.
Mr Ahmadinejad's letter also suggested that the opposition and Iran's enemies overseas had sought to exploit her death "for their own political aims and also to distort the pure and clean image of the Islamic Republic in the world".
President Ahmadinejad was declared the poll winner by a landslide, but his opponents said the victory was achieved by massive fraud.
The authorities reject the charge but Iran's top legislative body, the Guardians Council, has begun a partial recount of the poll - a move rejected by the defeated opposition candidate.
Meanwhile, UK Prime Minister Gordon Brown has demanded the release of British embassy staff detained by the Iranian authorities in Tehran.
Iranian officials say they have freed five of the nine staff and the rest are being interrogated.
Iran repeatedly accused foreign powers - especially Britain and the US - of meddling after the 12 June election.
Video appearing to show arrests following protests in Tehran on Sunday
In the fallout from the crisis, Tehran has expelled two British diplomats and the UK has responded with a similar measure.
At least 1,000 opposition supporters are reported to have staged a noisy rally outside a mosque in Tehran on Sunday evening before it was broken up by police and militia.
The report could not be independently verified because of reporting restrictions on foreign media.
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