Their request was declined by Lord Doherty, who said he was not satisfied there was a “cogent need” for an interdict.
However, the full hearing will now be heard next Tuesday, rather than Friday.
Lord Doherty said this was because it was in the interests of justice, and in the public interest, for the case – which is opposed by the UK government – to proceed as quickly as possible.
But he said: “I am not satisfied that it has been demonstrated that there is a need for an interim suspension or an interim interdict to be granted at this stage.”
The judge will not decide on the merits of the case until he has heard legal arguments from both sides on Tuesday, with his final ruling potentially being delivered the following day.
His decision not to grant an interdict was largely based on the fact that Parliament cannot be suspended until 9 September at the earliest.
The prime minister wants to suspend Parliament – a process known as proroguing – for five weeks ahead of a Queen’s Speech on 14 October.
The UK is due to leave the EU on 31 October, and the cross-party group of politicians involved in the case, including SNP MP Joanna Cherry and Liberal Democrat leader Jo Swinson, wants the court to rule that it would be illegal and unconstitutional for Mr Johnson to suspend parliament ahead of that date.
What has happened today is the parliamentarians, who were seeking an emergency injunction to lift the suspension of parliament, have lost that but there is to be a full hearing on Tuesday.
If they win that, then I think it is constitutionally significant and we really are in uncharted waters.
We could be in a position where we have a ruling that the advice given by Boris Johnson to the Queen, prompting her decision to prorogue parliament, was unlawful.
The government can appeal it, but pending any appeal it remains intact – so you are in a position where the monarch has made that order based on advice that is unlawful.
That would put the Queen in a very difficult position.
Speaking outside court, Ms Cherry challenged the prime minister to lodge a signed affidavit – a sworn statement on oath – with the court setting out his reasons for wanting to prorogue parliament.
Mr Johnson has insisted that the suspension of parliament is aimed at allowing him to set out a “very exciting agenda” of new legislation in the Queens’s Speech, and will not prevent MPs debating Brexit ahead of the UK’s departure.
Responding to Friday’s ruling, a UK government spokesman said: “As we have set out, the government needs to bring forward a strong domestic legislative agenda and MPs are not prevented from scrutinising our withdrawal from the EU.
“We are glad the court found against the interdict – there was no good reason to seek one, given the full hearing is due to take place next week, and the process of bringing the session to an end will not start until the week commencing 9 September.”
Meanwhile, Mr Johnson warned his political opponents on Friday that they are damaging his chances of getting a deal with the EU by trying to block a no-deal Brexit.
The Court of Session hearing came as former prime minister Sir John Major announced he was joining forces with campaigner Gina Miller to oppose the decision to suspend Parliament in the courts.
Ms Miller had already launched her own attempt, and Sir John said by joining her he would avoid “taking up the court’s time” by lodging a separate case of his own.
In Northern Ireland, proceedings at the High Court in Belfast by prominent Troubles victims’ campaigner Raymond McCord – who claims that leaving the EU without a withdrawal agreement would be an “unconstitutional attack on the people of Northern Ireland” – have been adjourned until next week.
Mr McCord is also seeking a ruling that the prime minister cannot “bypass” MPs by proroguing parliament.