Speaking in Parliament, prime minister Boris Johnson urged MPs to support it, explaining that it will "ensure the integrity of the UK internal market" when the Brexit transition period ends in December.
Johnson also said that the legislation will protect the Northern Ireland peace process and give more power to Scotland.
Speaking at Prime Minister's Questions, the PM said: "My job is to uphold the integrity of the UK but also to protect the Northern Ireland peace process and the Good Friday Agreement.
"And to do that, we need a legal safety net to protect our country against extreme or irrational interpretations of the Protocol, which could lead to a border down the Irish Sea, in a way that I believe would be prejudicial to the interests of the Good Friday Agreement and prejudicial to the interests of peace in our country. And that has to be our priority."
However, its critics have said that the bill will damage trust in the UK within the international community, after Northern Ireland secretary Brandon Lewis said that it would break international law in a "very specific and limited way".
Sir Jonathan Jones, the permanent secretary to the Government Legal Department, has also resigned from his position in the wake of the bill.
The bill will hand Scotland, Wales and Northern Ireland new powers to control issues related to air quality and building efficiency which are currently regulated by the EU.
A new Office for the Internal Market will also be established to ensure standards adopted in the four constituent UK countries will not undermine cross-border trade. It will also have the power to issue recommendations which are non-legally binding to Westminster and the devolved governments when there are discrepancies.
Following the publication of the bill, the PM’s official spokesman dismissed claims that the legislation would undermine devolution, saying: "What the devolved administrations will enjoy is a power surge when the transition period ends in December.
"There will be no change to the powers the devolved administrations already have and the vast majority of powers with devolved competencies returning from Brussels will go straight to Holyrood, Stormont and Cardiff Bay.
"This will be a significant increase in the powers of the Scottish Parliament, the Welsh Parliament, and the Northern Ireland Assembly, which are already among the most powerful devolved administrations in the world.
"Where powers are coming back to the UK Government this is to protect the economy."
The bill also outlines plans for UK ministers to have the right to apply customs and trade rules in Northern Ireland, which overrides the Northern Ireland Protocol outlined in the Withdrawal Agreement.
The European Commission is concerned that this element of the bill will mean that the UK will not deliver on the Withdrawal Agreement and has called an emergency meeting, while the Scottish government is also known to be in opposition.
European Commission president Ursula von der Leyen commented: "Very concerned about announcements from the British government on its intentions to breach the Withdrawal Agreement. This would break international law and undermines trust."
Senior Tories are also worried that pressing ahead with the bill could undermine the UK’s international standing. Tobias Ellwood, chair of the Commons Defence Committee, said that the nation will “lose the moral high ground” if the legislation passed through Parliament to become law.
The publication of the bill comes as negotiations over a post-Brexit trade deal continue in London this week.
Earlier on Wednesday, the prime minister confirmed new Covid-19 restrictions which will come into force in England from Monday, during a Downing Street news conference.
The newest measures will ban social gatherings of more than six people from September 14, with schools, workplaces, Covid-secure weddings, funerals and organised team sports exempt.
The previous rules allowed for gatherings of up to 30 people.
The move comes after a recent rise in the rate of infections and will bar larger groups of people meeting socially indoors or outdoors.
Overall, there have been 8,396 new cases reported since Sunday, with 2,460 of them coming on Tuesday.
£100 fines will be issued for breaches of the new law, doubling with every repeat offence up to a maximum fine of £3,200.
Health secretary Matt Hancock said: “One of the pieces of feedback we had including from the police was that we needed the rules to be super simple so that everybody knows what they are.
"And now this will now be rigorously enforced by the police.
"This is really simple. Gatherings are ok, they should be socially distanced of course, but groups only of up to six."
When asked by the media about people with symptoms experiencing difficulties accessing Covid-19 testing in recent days, Hancock said that large numbers of people that were ineligible for tests were coming forward to get one, resulting in a shortage.
"Unfortunately, we have seen this quite sharp rise in the last couple of weeks of people without symptoms who don't have a good reason coming forward and getting a test.
"I've even heard stories of people saying: 'I'm going on holiday next week therefore I'm going to go get a test'. No. That's not what the testing system is there for."
Meanwhile, Jonathan Bartley and Sian Berry have been re-elected as co-leaders of the Green Party, seeing off challengers Shahrar Ali and Rosi Sexton.
Bartley and Berry secured 49 per cent of the first preference votes, which dwarfed the 24 per cent and 27 per cent garnered by Ali and Sexton respectively.
In his acceptance speech, Bartley said: "The economic, climate and health crises have put the country at a crossroads -we can continue down the same old road or we can choose a transformative Green recovery that ensures the wellbeing of us all, now and in the future.
"Only the Greens have a clear, positive vision for what the country could be, and the ambition to build a grassroots mass movement which will demand, and work for, better than what came before."
Berry added: "We're growing fast - last year we doubled the number of Green councillors, and the 18 councils where Greens are part of the administration are among the most innovative and exciting in the country, but we can do so much more.
"Next year people will have a chance to bring real change to their area by electing more Green councils, putting Green voices in the Senedd, and electing a Green mayor for London."
Amelia Womack was also re-elected for a fourth term as the party’s deputy leader.
The Green party has one MP, Caroline Lucas, who has represented the Brighton Pavilion constituency since 2010. The Greens secured 2.7 per cent of the vote in last year’s general election, an increase on the 1.1 per cent it managed in 2017.
Elsewhere, the Conservative MP for Middlesbrough South and East Cleveland, Simon Clarke, has resigned from his government role at the Ministry of Housing, Communities and Local Government for personal reasons.
He was appointed as a minister for regional growth and local government in February following a move from the Treasury, but he will now relinquish this role and continue to serve in his capacity as an MP.
Clarke said in a letter to the prime minister that the move was down to personal reasons, explaining how he was in the process of “balancing my own life against the demands of office”, but hoped to return to government in future.
His letter read: "I would not have made this decision unless I believed it was of the utmost importance.
"It has been a privilege to serve as a minister in your administration."