Their lawyers told the court the extradition hearing was unfair because the Crown had deliberately restricted them from accessing funds to retain the services of US legal and technical experts.
Judge Dawson said the court had to balance the principles of the delivery of justice in a timely manner with the right of the parties to a fair hearing.
"This case has now been before this court for over three and a half years ... It is now the 10th time this case has been set down for hearing," Judge Dawson said.
The judge said the "interlocutory applications" by the defendants could be heard during the extradition hearing, rather than beforehand.
"The court would be better placed to rule on these applications having had the benefit of hearing the evidence of the eligibility hearing," Judge Dawson said.
The US Government's bid to extradite Dotcom will begin tomorrow.