Eugene Ohm, a lawyer representing Allen, said they had presented themselves as victims of the attack in public statements and that it would be “wholly inappropriate” for the pair to be directing the prosecution of this case.
The justice department was directed to respond to the request by 22 June.
Authorities have said Allen left his home near Los Angeles in Torrance, California, on 21 April, and travelled by train to Chicago before heading to Washington.
In a memorandum filed by the US government last month, prosecutors say Allen took photos of himself in his hotel room at around 20:03 EST (1:03 BST), wearing dress clothes as well as a shoulder holster, pliers and wire cutters.
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