"It is common ground that Mr Pora does not have a statutory right to apply for bail pending determination of his appeal by the Privy Council.
"His position is therefore in marked contrast to that of an appellant who has appealed against conviction or sentence to the New Zealand Court of Appeal or Supreme Court.''
The Bail Act permitted anyone who had lodged an appeal to those courts to be granted bail prior their appeal, however the act did not contain a similar provision for appeals to the Privy Council, Justice Lang said.
His application for bail was therefore dismissed.
Pora's lawyer Jonathan Krebs said the decision not to grant bail was "very thorough and reasoned".
"Obviously we're very disappointed. We went into the process aware it was going to be difficult," he said at a press conference this afternoon.
"I don't think it was a hopeful toss of the coin. It was a tricky application, it was complicated and we think it's certainly a valid argument."
He said Pora was "philosophical" about the decision.
"He's had a lot of knocks over the last 21 years... this is another one of those. Like us, Teina's focussing on what will happen in London later in the year.
"We have to focus on parole now. The parole hearing is on Monday and all of our efforts over the weekend will be going into that."
At his first trial in 1994, Pora was found guilty of the murder of Ms Burdett, who was beaten with a softball bat in the bedroom of her south Auckland home in 1992.
Pora had confessed to police but a retrial was ordered as doubts began to emerge about his involvement.
However, at the retrial in 2000, Pora was again found guilty.
After Pora's first trial, serial rapist Malcolm Rewa was convicted of raping Ms Burdett.
His DNA was found at the scene and at Pora's re-trial the Crown argued the two acted together.
But Pora's lawyer Jonathan Krebs said that ignored the fact they were associated with rival gangs and that Rewa had an erectile dysfunction problem.
That the re-trial jury was not told of Rewa's problem was down to error on the part of Pora's then lawyer, he said.
Pora is due to appear before the Parole Board on Monday and will face the Privy Council in October or November.