At the Court of Session in Edinburgh on Friday, opponents of the move made by the Prime Minister were denied an interim interdict to halt the prorogation of Parliament by judge Lord Doherty.
A decision was made to bring a full hearing forward to Tuesday from this Friday after the judge ruled it would be "in the interest of justice that it proceeds sooner rather than later".If an interim interdict had been granted it would have immediately lifted the royal order to suspend Parliament.
A full interdict could still be granted by the judge.
The judge will not decide on the merits of the case until he has heard legal arguments from both sides, with a final ruling potentially being delivered on Wednesday.
A request was also made by the petitioners on Friday that the Prime Minister issue a legally binding statement to the court - known as an affidavit - over his reasons for the suspension.
This is not automatically granted but if it was the Prime Minister could potentially be called to face cross-examination.
Speaking outside the court on Friday, SNP MP Joanna Cherry QC - one of the campaigners behind the legal action - urged the Prime Minister to "tell the truth, have the courage of your convictions - swear on oath your reason for prorogation".
Labour MP Ian Murray, who is also backing the action, said Tuesday's hearing would make this week "the most important week in modern British history".
Tuesday will also see a victims' campaigner in Belfast resume his own legal bid to block the suspension of Parliament.
Raymond McCord's lawyers will urge a High Court judge to convene a hearing later in the week on an application to injunct prorogation.
The campaigner, whose son Raymond Jnr was murdered by loyalist paramilitaries in 1997, is already taking judicial review proceedings against the Government to prevent a no-deal
Brexit, claiming a disorderly exit would damage the peace process.
The hearing on that wider issue is listed to take place on September 16.
Mr McCord hopes to secure an earlier discrete hearing, potentially on Friday, on the injunction bid ahead of the full hearing on the no-deal Brexit challenge.