Mr Peters said he had asked for evidence two months ago, after Mr Horan's brother had phoned him but he had received no evidence to date.
"I did leave that conversation on the basis that he would get me the information and pronto,'' said Mr Peters.
"This is a priority matter and it's urgent.''
Mr Horan was on leave until Mr Peters had viewed bank statements and other evidence.
Mr Ormsby, said the bank statements showed a large number of withdrawals from TABs and from ATM machines near Mr Horan's office in Mount Maunganui, Auckland and Hamilton.
They also showed numerous payments at takeaway food outlets and video shops.
Mr Ormsby has said his initial investigation suggests about $85,000 was missing from his mother's account.
Mr Horan has said firmly he will not step down from NZ First because of the matter. He called in lawyers after an article was published revealing the allegations.
Mr Horan's mother, Olwen Horan, 87, of Mount Maunganui, died in early August about three months after signing a codicil to her will, after becoming concerned that money was missing from her accounts.