Boris Johnson has said he will “wait and see what the judges say” before deciding whether to recall Parliament.
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 said 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.
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.
Speaking to BBC political editor Laura Kuenssberg ahead of the court case later, Mr Johnson said he had the “greatest respect for the judiciary”, and its independence “is one of the glories of the UK”.
“And I think the best thing I can say, having said that, is to wait and see what they say,” he said.
Asked again if he would be ready to recall Parliament if that was what the Supreme Court said he ought to do, he said: “I think the best thing I could do is wait and see what the judges say.”
The hearing is scheduled to last until Thursday.