Remain campaigners argued at the Court of Session in Edinburgh on Monday that, although he had undertaken not to frustrate the purpose of the so-called Benn Act, Mr Johnson was “sailing close to the wind”.
Judges will reconvene at a date to be confirmed.
Elaine Motion, solicitor at Balfour+Manson, which is representing campaigners who brought the challenge, said: “From our perspective it was a great success again for us.
“Because the court have kept hold of this case, they’ve kept it live to make sure that the prime minister continues to comply with the Benn Act and all of the obligations under it.”
The prime minister sent a letter to the EU asking for an extension to Article 50 on Saturday, as required by the Benn Act.
This legislation was passed by MPs to try and avoid a no-deal Brexit at the end of this month.
However, Mr Johnson did not sign that letter and sent a second one – which he did sign – in which he said that a delay would be a mistake.
Campaigners concerned that the PM would not comply with the Benn Act launched a legal challenge to try and get him to do so.
In the case’s first hearing on 9 October, lawyers for the government assured the court that Mr Johnson would adhere to the law in writing and before the judges – despite his repeated public statements that he would never ask for a delay.
The case was then postponed until after the deadline for the extension letter to be sent under the terms of the Benn Act.
In the hearing on Monday, it was accepted that Mr Johnson had observed part of the legislation by sending the request letter to the EU, even though it was unsigned and accompanied by the second letter.
Petitioners – including businessman Dale Vince, Jolyon Maugham QC and SNP MP Joanna Cherry QC – have been granted a request by the judges to postpone any decision to see if the terms of the Benn Act have been fully carried out.
This includes waiting to see if any potential extension granted by the EU is accepted by the prime minister.
Aidan O’Neill QC, representing the petitioners, said the manner in which the request to delay Brexit was made was “unusual”.
He continued: “We don’t know when the EU will come back with a response for the request.
“So it depends on it coming back and ensuring the prime minister carried out the duties imposed upon him within the Benn Act.”
Mr O’Neill claimed that the PM had breached the principle that he would not try and frustrate the purposes of the legislation, but added that this would be for the court to decide at a later date.
Judge Lord Brodie said: “I think it is fair to say it was a very carefully written letter.”
Mr O’Neill also told the court that Mr Johnson was “sailing very close to the wind” and “not entirely in accord with spirit” of the Benn Act by sending the second letter.
David Johnston QC, representing the UK government, said the appeal should be dismissed as the letter had been sent.
The court said it would return to the matter at a later date, although the case could be made null if Mr Johnson manages to get his Brexit deal passed by MPs.
Judge Lord Carloway said the decision would be delayed under similar terms to those in previous hearing.
He said: “The court considers that the case should be continued until clear that the obligations under the 2019 Act have been complied with in full.”