Boris Johnson, who is flying back early from a UN summit in New York, faces calls to resign from opposition groups.
The PM has said he “profoundly disagreed” with Tuesday’s landmark ruling but he would respect it.
Chancellor of the Duchy of Lancaster, Michael Gove, said he would not criticise the court, but he “disagreed with their position”.
Commons Speaker John Bercow said MPs will sit from 11:30 BST. There will be no Prime Ministers’ Questions but urgent questions, ministerial statements and emergency debates would be heard.
Mr Gove also said the government would outline its approach to the court ruling later through the Leader of the Commons, Jacob Rees-Mogg.
Following Tuesday’s unanimous ruling, Labour leader Jeremy Corbyn brought forward his party conference speech so he could return to Westminster on Wednesday.
Speaking to BBC’s Radio 4 Today programme, he reiterated his call for Mr Johnson to resign, and said the court’s decision had left the PM “badly wanting”.
But he said he would not be proposing a motion of no confidence, which could trigger a general election, until it was “very clear” the prime minister will seek an extension to Brexit to prevent a no-deal.
On Tuesday, the court ruled it was impossible to conclude there had been any reason – “let alone a good reason” – to advise the Queen to prorogue Parliament for five weeks in the run-up to the Brexit deadline of 31 October.
Mr Johnson, who was attending the UN General Assembly in New York, spoke to the Queen after the ruling, a senior government official said, although no details of the conversation have been revealed.
The prime minister also chaired a 30-minute phone call with his cabinet.
A source told the BBC Mr Rees-Mogg told cabinet ministers on the call that the action by the court had amounted to a “constitutional coup”.
The one thing we can be sure of is the government is going to face a barrage of criticism from all sides of the House of Commons later.
As a member of the cabinet said to me, Parliament and the opposition will now be able to keep the government as political hostages and almost play with them in their agony.
But it is quite something to hear a senior member of government, run by the Conservative and Unionist Party – whose principals have always been about trying to preserve the status quo and respecting the country’s institutions – still saying they don’t believe they did anything wrong.
You can see how No 10 are trying to play all of these things. We have seen it time and again that the response of this government is to double down when things go wrong.
But increasingly there is unease among ministers in government about this approach and there is unease in the Tory party.
It may well, in time, play to their Brexit-backing bases, but, my goodness, this is risky.
Some people believe that strategy is not just speeding them towards being able to keep their promise over Brexit – it may also speed them towards crashing into a brick wall.
But we will only know in time, when the public give their verdict, if that is a strategy that will crash and burn or whether it is something they can use to their advantage.
Speaking after the ruling, Mr Johnson insisted the suspension of Parliament had been necessary in order for him to bring forward a Queen’s Speech on 14 October outlining his government’s policies.
But the court found that the effect of such a move stopped MPs from scrutinising the government.
Earlier, the prime minister said he “refused to be deterred” from getting on with “an exciting and dynamic domestic agenda” and to do that he would need a Queen’s Speech.
The court ruling does not prevent him from proroguing again in order to hold one, as long as it does not stop Parliament carrying out its duties “without reasonable justification”.
A No 10 source said the Supreme Court had “made a serious mistake in extending its reach to these political matters” and had “made it clear that its reasons [were] connected to the Parliamentary disputes over, and timetable for” Brexit.
But Supreme Court president Lady Hale emphasised in the ruling that the case was “not about when and on what terms” the UK left the EU – it was about the decision to suspend Parliament.
Mr Johnson has said Brexit will happen with or without a deal on 31 October.
But MPs passed a law before Parliament was suspended to force the PM to ask for an extension from the EU if a deal – or approval for no-deal – is voted for by MPs by 19 October.
Speaking to Today, Mr Gove said he “appreciated the gravity” of the decision by the Supreme Court, but he disagreed with their position.
He said: “It is only fair to point out that there is a very respectable set of legal opinions that have pointed out, according to the understanding of the law – until now – what the government did was entirely lawful.
“Now, of course, the Supreme Court has taken a different view and I think it is all important we reflect on that judgement and its consequences.”
Pushed on whether the government would apologise, Mr Gove said they should not say sorry for “having a strong domestic agenda” and seeking a Queen’s Speech.
Instead, he reiterated calls for Parliament to agree to hold a general election and “let the people decide”.
Mr Corbyn said he would not back an election “until it is very, very clear” the prime minister will seek an extension to Brexit to prevent a no-deal, and so far he has “refused to give the undertaking to do that”.
He told Today that preventing the UK leaving without a deal was Labour’s “priority”, adding: “I am very happy to have a general election when we have taken no deal off the table and the European Union has agreed that extension.”
The Labour leader also called on Mr Johnson to apologise for suspending Parliament in the first place.
“He should apologise both to [the Queen], but more importantly apologise to the British people for trying to shut down our democracy in a crucial time when people are very worried about what will happen on 31 October,” he said.
Asked whether he would vote for a recess to allow the Conservatives to hold their own conference later this week, Mr Corbyn said: “I won’t support anything that shuts down Parliament until it is absolutely clear the government will abide by the European Union law that we passed in Parliament [ruling out a no-deal Brexit].”
‘He’s not going anywhere’
Scotland’s First Minister, the SNP’s Nicola Sturgeon, Wales’ First Minister, Labour’s Mark Drakeford, and Sinn Fein’s vice-president, Michelle O’Neill have all called for Mr Johnson to resign.
Downing Street has insisted there is no question of him standing aside.
And Mr Johnson was backed by US President Donald Trump at a joint press conference at the UN summit.
“I’ll tell you, I know him well, he’s not going anywhere,” said Mr Trump, after a US reporter quizzed the prime minister on whether he was going to resign.