"We will respect the law and we will come out on October 31", Johnson told ITV.
However, Johnson has only been in office since July and is likely to resist such calls. Johnson says he won't quit.
Labour leader Jeremy Corbyn told BBC Radio 4's Today program that Johnson's Tory government should not "be able to run away from accountability yet again".
The former coalition minister ruled out pushing for a vote of no confidence in the Government until that deadline is moved. He said he would make time for such a vote on Thursday.
Rachel Johnson appears on Sky News' The Pledge.
If that failed, there would be an election.
Mr Johnson replied: 'Of course there will be an attempt to try to obfuscate the effect of this Act, but it does - the Capitulation Act, or the Surrender Act or whatever you want to call it - it does, I'm sorry, but it surely significantly enfeebles, it significantly enfeebles this Authorities's skill to barter.
Earlier this month lawmakers twice rejected a call for a snap poll.
The opposition warns a no-deal Brexit would be highly disruptive for Britain's economy and have said Johnson should first delay Brexit before an election is held.
Guy Verhofstadt said after a meeting with Brexit negotiator Michel Barnier that United Kingdom proposals on how to better deal with the border between Ireland, which is in the European Union, and the U.K.'s Northern Ireland do not preserve consumer safety, do not protect EU businesses and would not preserve peace in the volatile region.
Belgian MEP Guy Verhofstadt told an European Union parliamentary committee that the alternatives offered were "not meeting" the benchmarks the European Union has set out for an orderly British exit.
The prime minister is facing an angry backlash at home for his dismissive response to MPs complaining about his rhetoric and citing the fate of a colleague murdered by a far-right extremist during the Brexit referendum campaign.
He goaded his opponents either to bring down the government or get out of the way to allow him to deliver Brexit.
Attorney General Geoffrey Cox also faced questions about his legal advice that indicated the five-week suspension would be within the law.
He added: "Just to reiterate this is about the role we all play".
Johnson is expected to return to London for the resumption of parliament on Wednesday.
Parliament opened Wednesday morning, one day after the landmark ruling.
The House of Commons speaker John Bercow has described the atmosphere in the House of Commons yesterday as "toxic". He says he will not step down.
Johnson has said he is aiming to reach a deal with Brussels ahead of October 31 but is ready to take Britain out of the European Union without a deal if necessary. Johnson says Britain will leave on that day with or without a deal.
Mr Johnson was forced back to Westminster, cutting short his visit to the United Nations General Assembly in NY, after the Supreme Court ruled on Tuesday his five-week suspension of Parliament was illegal.
The law would apply whether or not Johnson remains.
Speaking in NY yesterday, Leo Varadkar said Ireland would be "open to granting an extension" if asked.
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