Mr Horan was stood down last week by New Zealand First leader Winston Peters, who told him to return to Tauranga to provide evidence to clear his name.
The allegations came from Mr Horan's brother Mana Ormsby, who said bank statements showed a large number of withdrawals from TABs and ATM machines near Mr Horan's office in Mount Maunganui, Auckland and Hamilton.
An initial investigation suggested about $85,000 was missing from his mother's account, he said.
The statement from Mr Horan's lawyer Paul Mabey, QC, today said various issues had arisen concerning the administration of his mother's estate as a result of her death.
"Those matters are private and personal to the family. Unfortunately some persons, for their own reasons, have chosen to make them public.
"Mr Horan has been the subject of unwarranted and unfair publicity which has implied that he is dishonest and has stolen from his mother. There can be no other interpretation of that publicity," the statement said.
"Mr Horan completely denied any suggestion that he has stolen from his mother or misappropriated her money or assets. He regrets that a private and personal family matter has been made public and his only wish is that the issues concerning his mother's estate are resolved quickly and properly. He invites any investigation into his mother's affairs and is confident that any proper investigation will exonerate him entirely."
Mr Horan would make no personal comment but looked forward to the matter being resolved so he could return to his work as an MP "without the distraction of false and unjustified allegations".