The PM sent a letter requesting the delay, in accordance to the Benn Act which aims to prevent no deal, but did not sign it.
He also sent a letter in which he said he felt an extension was a mistake and insisting the request was from Parliament.
Edinburgh's Court of Session is looking into the legality of his actions, with the Government insisting he has followed the law and the case should be dropped.
However, judges today refused to close the case until they are satisfied the Benn Act is adhered to in its entirety.
The Benn Act also states the government must accept any delay to Brexit that is offered.
Brexit is currently due to take place on October 31.
Jolyon Maugham, a lawyer involved in the case, said on Twitter: "I am delighted with the Court's decision. It is a pity to have to say it, but this is not a Prime Minister who can be trusted to comply with the law.
"And because he cannot be trusted he must be supervised."
It comes after the Lord Chancellor Robert Buckland said the three letters meant the Government had abided by the act.
While Lord Pannick QC said the Prime Minister "just about" acted lawfully in asking the EU for a Brexit delay.
The peer told BBC Radio 4's Today programme: "I think the Prime Minister is on the right side of the law on this occasion.
"The Benn Act required him to send a letter to the president of the European Council seeking an extension and that's what he's done. The Act doesn't require that he's signed the letter.
"My view is that he's on the right side of the law - just about - on this occasion."