The Supreme Court will hear two appeals that will determine whether the prime minister acted lawfully in suspending Parliament for five weeks.
Edinburgh’s Court of Session says that the shutdown was unlawful and London’s High Court said it was not a court matter.
On Monday the PM visited Luxembourg for Brexit talks, but the EU said it was yet to see concrete proposals.
Mr Johnson pulled out of a joint press conference with Luxembourg Prime Minister Xavier Bettel, blaming noisy protesters, but Mr Bettel went on to criticise Mr Johnson’s approach to Brexit.
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The suspension of Parliament, a process known as proroguing, began a week ago.
MPs are not scheduled to return until 14 October, when there will be a Queen’s Speech outlining Mr Johnson’s legislative plans. The UK is due to leave the EU on 31 October.
Opposition parties have called for Parliament to be recalled.
Asked again if he would be ready to recall Parliament if that was what the Supreme Court said, “I think the best thing I could do is wait and see what the judges say.”
The hearing is scheduled to last until this coming Thursday.
Justice Secretary Robert Buckland told BBC Breakfast that whatever the Supreme Court’s decision, the “robust independence of our judiciary must be respected”
He added, “It would be wrong of me to anticipate what their lordships might say, I’d simply say this: We will examine the ruling very carefully and abide by the rule of law.”
Speaking to the BBC yesterday Mr Johnson said the EU had “a bellyful” of the Brexit process and wanted to get a deal, adding that leaders were “fed up with endless delays” and wanted to move onto the next phase of talks on future relations.
But on Monday Luxembourg’s PM attacked the prime minister’s approach to Brexit, calling the situation a “nightmare”.
Eleven of the Supreme Court justices will hear legal arguments from the English and Scottish court cases. The government’s lawyers will then respond.
BBC legal affairs correspondent Clive Coleman said it was only the second time 11 justices would sit – the first time this happened was in a challenge as to whether the prime minister or Parliament should trigger Article 50 to start the process for leaving the EU.
He added that they will determine whether prorogation is a matter for the courts.
If they decide it is, they will go on to rule definitively on whether Mr Johnson’s true motive in advising the Queen was to undermine MPs’ ability to legislate and respond to events as the country prepares to leave the EU, our correspondent added.
This will determine whether Parliament is recalled.