A High Court ruling on Wednesday had set up Liverpool to be sold for 300 million pounds to New England Sports Ventures (NESV), before Gillett and Hicks obtained a temporary block in a Texas district court.
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That case was adjourned and will resume at 12:00GMT Friday - three hours before the British High Court's deadline for the American duo to comply with their ruling.
In front of the same Judge, Mr Justice Floyd, who ruled in their favour on Wednesday, they sought an injunction to stop the club's American owners continuing with their U.S. legal action.
"It is an abuse of process, unconscionable and an affront to justice... a plain attempt to frustrate and impede the proceedings," the Press Association reported Richard Snowden QC, for the bank, as saying.
"Plainly it is a bid to frustrate this court in the exercise of its jurisdiction."
Snowden added that Hicks and Gillett's claim that they were victims of an "epic swindle" and "grand conspiracy" over the club's sale were "wild and scurrilous" assertions with no evidence to support them.
The Judge found in the bank's favour, saying that his ruling was not aimed at the Dallas court but at Hicks and Gillett and gave the duo until 15:00GMT on Friday to comply with his orders.
"The owners' behaviour conclusively demonstrates just how incorrigible they are," he said. "They are absolutely determined to stop this transaction in its tracks and they have no lawful justification for behaving in this way."
"It has become clear to me that the Board is intent on selling the club to NESV to the exclusion of all other parties, regardless of the merits of their bids," the Singapore businessman said in a statement.
If RBS and the Liverpool board thought that their High Court victory and the strong words of the judge would force Hicks and Gillett to cave in, they soon found otherwise as the duo, who on Wednesday claimed $1.6 billion in damages, immediately filed a motion for contempt."
The motion asked for the "incarceration of defendants until they cure themselves of contempt and fine the defendants for their actions" and requested a daily fine of $50,000 be imposed until the contempt of court was ended.
