Allowing ministers to trigger Brexit was Parliament's "clear expectation" when it agreed to an EU referendum, the Supreme Court has been told.
Attorney General Jeremy Wright said the government would be making "lawful" use of "fundamental" powers by triggering Article 50 of the Lisbon Treaty.
He was speaking at a legal hearing into whether Parliament's consent was needed before Brexit negotiations begin.
The High Court ruled in October that MPs did need to give the go ahead.
The government is appealing against that decision, with the hearing expected to last four days and a verdict due in January.
The outcome will have implications for Theresa May's strategy for EU exit, but it is not a court case on whether or not Brexit actually takes place.
In the first session at the Supreme Court:
- Court president Lord Neuberger said the judges would consider issues impartially and decide the case according to the law
- The government set out why it thinks it should be able to use "prerogative powers" to trigger Brexit
- Ministers have the power to make or unmake treaties, it said
- It said the powers were not a "relic" but a key part of the constitution
- Parliament could have chosen to restrict ministers' power to act but had chosen not to, it said
At the start of the hearing, Supreme Court president Lord Neuberger said the justices were aware of the public interest in the case and the "strong feelings associated with the many wider political questions surrounding the United Kingdom's departure from the European Union".
But he added: "This appeal is concerned with legal issues, and, as judges, our duty is to consider those issues impartially, and to decide the case according to the law."
He also said some of the people involved in the case had received "threats of serious violence and unpleasant abuse in emails and other electronic communications", warning anyone that such behaviour "undermines the rule of law".
The UK voted to leave the EU, by a margin of 51.9% to 48.1%, in a referendum in June.
Image captionSupreme Court president Lord Neuberger said the court was aware of the public interest in the case
The prime minister has said she intends to officially notify the rest of the EU of the UK's intention to leave - beginning two years of talks over the terms of separation - by the end of March.
But campaigners, led by investment manager Gina Miller and hairdresser Deir Dos Santos, insist that decision can only be taken by Parliament.
The BBC's Clive Coleman said it was an "extraordinary" atmosphere at the Supreme Court in Westminster, with people queuing to get in from early morning, demonstrators dressed as judges and the world's press gathered outside.
Media captionWhat will the Supreme Court be considering in the Article 50 case?
The BBC's legal correspondent Clive Coleman summarises the points at stake
- The case is about whether the law means that the government needs the authority of Parliament to trigger the process for the UK to leave the EU
- The government argues it can start the Article 50 process using "prerogative powers", a remnant of the era of all-powerful kings and queens
- Justices will be ruling on who has the legal power to change the rights of British citizens
Monday's hearing began with Mr Wright setting out the government's case.
He said the "royal prerogative" powers the government wants to use to trigger Article 50 were not an "ancient relic" but a "fundamental pillar of our constitution as a sovereign state".
The government did not seek to use the prerogative "on a whim", he said.
Mr Wright said the legislation enabling the EU referendum had been passed with the "clear expectation" that the government would implement the result, and that Parliament had had the opportunity to restrict the government's power to trigger Article 50 but had chosen not to do so.
"If this is all about standing up for Parliament, I say Parliament can stand up for itself," he said.
Image captionGina Miller says she has received death threats after bringing the case
Image captionAttorney General Jeremy Wright is representing the government
The High Court ruled in Ms Miller's favour, arguing that rights conferred by Parliament when it passed the 1972 European Communities Act - which paved the way for the UK to join the then European Economic Community - were likely to be affected by Brexit.
As a result, it concluded, any process leading to the potential withdrawal of rights could only be determined by Parliament.
In its judgement, the High Court ruled "the powerful constitutional principle that the Crown has no power to alter the law of the land by use of its prerogative powers is the product of an especially strong constitutional tradition in the UK".
The ruling led to criticism from some elements of the press and Brexit-supporting MPs, but in her submission ahead of Monday's hearing, Ms Miller said the Court had a "duty to decide questions of law".
Labour has said it will try to amend an Article 50 bill - if one is required - to ensure single market access and workers' rights are protected.
But shadow attorney general Baroness Chakrabarti said her party would not try to veto Brexit.
She told BBC Radio 4's Today programme: "We have been completely clear that we are democrats and respect the outcome of the referendum, even though many of us - myself included - campaigned in the opposite direction.
"So this will happen, pursuant to the will of the people. But there is not a simple question of 'in and out of the European Union', there are many questions that Parliament has to scrutinise about what happens next."
Image captionSome protesters - and their pets - came to the Supreme Court ahead of the hearing
Ministers will have a number of options if they lose the appeal, but it has been reported that a 16-word bill is being prepared which could be fast-tracked though Parliament, asking MPs and peers "to give permission" to the government to trigger Article 50 in time to meet the March deadline.
The respective legal teams will be led, on the government side, by Attorney General Jeremy Wright while crossbench peer Lord Pannick will head the team acting for Ms Miller.
How to follow the court hearing
- Monday's hearing is scheduled to run from 11:00 GMT until 13:00 GMT and from 14:00 GMT until 16:30 GMT
- Watch a live stream on the BBC website, along with rolling updates and analysis
- Transcripts are being published twice a day by the Court by 16:00 GMT and 19:00 GMT
The case is one of the most keenly anticipated of its kind in recent history. Additional seating has been provided to allow 115 members of the public to watch proceedings while more than 80 journalists from around the world have been accredited to cover the event.
The court will also consider two separate but connected legal challenges to the exercise of prerogative powers brought by Northern Irish campaigners.
And in another twist, the Scottish and Welsh Governments have been granted permission to intervene in the case to establish matters of important legal and constitutional principle, including the basis on which the Article 50 process might need to be sanctioned by their devolved legislatures.
Other interested parties and intervening groups - who will be making oral arguments before the court - include citizens of EEA countries living in the UK known as AB parties and Grahame Pigney's crowd-funded People's Challenge.