A judge at London's High Court in July comprehensively ruled against Harry, singer Elton John and other British figures, rejecting allegations that the Mail titles had engaged in widespread unlawful activities, such as phone hacking.
The prince, 41, described the ruling as a "complete and obvious whitewash", while Associated said it was an overwhelming victory for its newspaper and journalists, and "for a free press generally".
At a hearing on Wednesday to determine liability for legal costs, Associated's lawyer Antony White argued that Harry and the other claimants should pay costs on an indemnity basis, under which the losing party must cover the other side's charges without the need to show they were proportionate.
In a scathing attack on the claimants' case, which he said had been designed to create "a banquet of litigation" against Associated, White argued they had made wide-ranging and serious allegations without supporting evidence.
In written submissions, Associated sought an interim payment of nearly Stg10 million.
Lawyers for the claimants said in their submissions that Associated had reported incurring "a simply extraordinary Stg34.5 million" in costs, far exceeding its agreed budget.
They offered an interim payment of Stg8 million by August 28 and said the claimants had insurance cover of up to Stg16 million.
"Of course, the (claimants) accept that their claims have been dismissed and it is appropriate that an order for costs on the standard basis follows the event," the submission said.
"But the further penalty of an indemnity costs basis order is not one which, in all the circumstances, should be imposed."
In his ruling, Judge Matthew Nicklin said the claimants had needed to prove that information published about them had been obtained unlawfully, but had failed to do so, and that suspicion alone was not enough.
