Mark Karpeles had been asked to attend a hearing in Washington on Friday.
MtGox reported in February that it may have lost nearly $500m (Â£300m) worth of the virtual currency and subsequently filed for bankruptcy protection in Japan and the US.
It later said it had "found" about a quarter of the missing sum.
A US judge ordered Mr Karpeles to travel from Japan to appear in front of the US Department of Treasury's Financial Crimes Enforcement Network to answer questions about the affair.
But a court filing by MtGox's lawyers said the France-born chief executive - who has not been charged with any crime -  would not comply.
"Mr Karpeles is now in the process of obtaining counsel to represent him with respect to the FinCen subpoena," it said.
"Until such time as counsel is retained and has an opportunity to 'get up to speed' and advise Mr Karpeles, he is not willing to travel to the US."
The lawyers also asked the court to delay Mr Karpeles' deposition until 5 May, but added that they could not guarantee he would attend on that date either.
In the meantime MtGox's site continues to tell out-of-pocket investors that a "method for filing claims will be published on this site as soon as we will be in [a] situation to announce it".
One bitcoin is currently trading for about $500, down from its high of more than $1,100 last year.
MtGox's founder has refused a US court's demand that he testify this week about the collapse of what was the world's biggest Bitcoin exchange.