Mr Peters also refused to provide the time-frame he'd given Mr Horan to front up with evidence, or when Mr Horan would return to Parliament. He said Mr Horan was still carrying out his Parliamentary duties while not in Parliament.
"He's doing all his constituency work, he's doing all his correspondence. He's not on beach leave, or on gardening leave; he's getting on with his job.
Mr Horan confirmed on Monday he had received strict instructions from Mr Peters, but would not say what he was told to do.
"That's between Winston and I, and I have no comment to make," he said.
When asked when he would be back to continue his duties in Parliament, Mr Horan replied: "If the media would leave my family alone it would be as expeditiously as possible."
He would not say why there had been more than two months' delay in providing information to Mr Peters.
"I'm not the person holding things up here," he said.
"It's a personal family matter. It should never be in the media spotlight."
Mr Horan's brother Mana Ormsby, the executor of the will and a lawyer, said the bank statements showed a large number of withdrawals from TABs and 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 suggested 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.