Justice Minister Patrick Chinamasa told AFP he had filed papers yesterday that sought "a postponement of the date for the harmonised elections from July 31, 2013 to August 14, 2013."
The announcement comes just days after Southern African leaders pressed Mugabe to delay the polls to allow more time for democratic reforms.
In setting the original election date, Mugabe had said he was complying with the constitutional court's ruling to hold elections by July 31.
Prime Minister Morgan Tsvanigirai, a long-time Mugabe rival, has called for reforms -- to free the media, depoliticise the security services and make sure the electoral roll is accurate -- before the vote is held.
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It was not immediately clear whether the court would grant the extension, or whether two more weeks will be enough to see Tsvangirai's demands met.
Leaders from the Southern African Development Community had on Saturday issued an unusual rebuke of Mugabe, asking that he go back to the court and seek a delay.
"During proceedings at the said summit, I, in particular was directed to make an urgent application before this honourable court to seek a postponement," Chinamasa's filing read.
"In my capacity as the minister responsible for the administration of the electoral act, I pray for an order for the extension of the elections to the 14th of August.