Fifa president Gianni Infantino "strongly disapproves" of the breakaway European Super League and says the 12 clubs will have to "live with the consequences" of their decision to join.
Premier League clubs Arsenal, Chelsea, Liverpool, Manchester City, Manchester United and Tottenham are part of the proposed league.
"There is a lot to throw away for maybe a short-term financial gain for some," said Infantino.
"Either you are in or you are out."
Meanwhile, UK Prime Minister Boris Johnson met with the Football Association, Premier League officials and fans' representatives on Tuesday, after which the government said it will take "whatever action necessary", including legislative options, to ensure the proposals were stopped.
Johnson's stance is supported by Labour and the Liberal Democrats.
A statement released after a meeting between the Premier League and the 14 clubs not involved said they "unanimously and vigorously" rejected plans for the competition.
It added that it is considering "all actions available" to stop the competition and asked the six teams to end their involvement immediately.
The Football Supporters' Association has met with the government and the Labour Party to discuss the impact of the breakaway league.
In other developments on Tuesday:
- Uefa president Aleksander Ceferin called on the English clubs to "come to your senses"
- Everton criticised the "preposterous arrogance" of the clubs involved
- Real Madrid president Florentino Perez said the new league was needed to "save football"
The proposed tournament would see teams play one another in midweek games in an attempt to have more matches between big-name clubs.
The other clubs involved are AC Milan, Atletico Madrid, Barcelona, Inter Milan, Juventus and Real Madrid.
"It is our task to protect the European sport model. If some elect to go their own way, they must live with the consequences of their choices," said Infantino, head of world football's governing body.
"They are responsible for their choice completely. This means you are either in or you are out. You cannot be half in and half out."
What have managers & players said?
Manchester City manager Pep Guardiola said he is "uncomfortable" talking about the competition, which he only found out about on Sunday.
"It is not a sport if success is guaranteed or if it doesn't matter when you lose," he told a news conference.
"I have said many times I want a successful Premier League, not just one team at the top.
"Sport is not sport when the relationship between effort and reward does not exist."
The ESL would guarantee a spot for the founding teams, meaning there would be no relegation or uncertainty over big names qualifying for the competition.
Leicester City and former Liverpool boss Brendan Rodgers says the competition shows football is prioritising business over sport.
"We must never lose the fact it is a sport and is a game for supporters and players. That always has to be at the forefront of any decision," he said.
"The six teams who are there can never forget the brand of the Premier League is based around all the teams.
"The roots of their success are based around the other teams because of the competition: the bottom team can beat the top team."
Fans, Uefa, German FA and other European sides react
There have been protests outside the grounds of the Premier League clubs who have signed up to the league.
Leeds players also wore T-shirts saying 'Earn it' next to the Champions League logo and 'Football is for the fans' before their 1-1 draw with Liverpool on Monday.
On Tuesday, Ceferin called on the English clubs to "come to your senses".
Directly addressing the owners of the six Premier League clubs, he said: "Gentlemen, you made a huge mistake. There is time to change your mind.
"Come to your senses. Not out of love for football - I don't imagine you have much of that - but out of respect for the people who bleed for the team, out of respect for the home of football. I know we are right and they are wrong. It is a match we cannot lose."
The president of the German Football Association (DFB) said the 12 clubs should be banned from all competitions.
No German club has signed up to the ESL.
"Football is open and it is there for everyone. A closed Super League on the other hand is only for the super rich and the super ruthless," Fritz Keller said.
Current European champions Bayern Munich rejected the notion of a Super League and expressed their solidarity with the Bundesliga.
"On behalf of the board I can expressly state that FC Bayern does not take part in the Super League," said chairman Karl-Heinz Rummenigge.
"For FC Bayern, the Champions League is the best club competition in the world."
French Ligue 1 champions Paris St-Germain have also not joined the Super League, saying the club is "a family and a community whose fabric is our fans".
PSG chairman and chief executive Nasser Al-Khelaifi added: "We believe any proposal without the support of Uefa - an organisation that has been working to progress the interests of European football for nearly 70 years - does not resolve the issues currently facing the football community, but is instead driven by self-interest."
What have other Premier League clubs said?
In a lengthy statement, the Everton board said the six clubs were "tarnishing the reputation of our league and the game", accused them of "disrespect" towards fellow Premier League clubs.
The statement added: "This preposterous arrogance is not wanted anywhere in football outside of the clubs that have drafted this plan."
Real Madrid president Perez said the new league was needed to "save football" and help recoup losses caused by the coronavirus pandemic.
However, Everton have accused the six Premier League clubs of acting "entirely in their own interests".
Leicester City, shock Premier League winners in 2015-16 after just avoiding relegation 12 months earlier and who spent a decade outside the top flight before that, said "solidarity and unity" is needed to "protect the future" of football.
Brighton said the breakaway league showed "a clear lack of respect" for other sides and that it would "destroy the dreams of clubs at every level".
A statement read: "These plans are the latest in an alarming and growing list of clandestine attempts from a small group of clubs whose actions would be wiping out close to 150 years of football's tradition."
Burnley have called on the government to introduce an independent regulator to protect English football through legislation.
West Ham, who are chasing a Champions League place for next season, said the proposals "go totally against the ethos and values" of the club and were an "attack on sporting integrity".
West Brom said they "wholly oppose" the "selfish and divisive plans" that "no genuine football fan" can support.
Wolves accused the owners of the six clubs of having "plotted and schemed to find a way to exist in a small and comfortable bubble" and that they have "united the whole of the football world against them".
Fifa said in January that players involved in a breakaway league would be barred from international competitions.
Agent Jonathan Barnett, who represents Wales and Tottenham forward Gareth Bale, said he would go to court if such a ban was introduced.
"The only people who are really going to suffer inside the business is players," Barnett told Radio 4's Today programme.
"I've been speaking to Fifpro [the players' union] and I assure you, we will go to court to fight the rights of the players."
BBC sports editor Dan Roan
The backlash is growing - there are more protests outside Stamford Bridge now. Fans often divided are now united.
The 14 other teams met on Tuesday to discuss how they could block it. The rebels insist they are helping football.
The consequences could be seismic - players warned they could be banned from the World Cup. This could be the natural conclusion of growing billionaire owners in the game.
The government has said it would consider legislation to block the proposals.
The disapproval of Manchester City manager Pep Guardiola highlights the tension and divisions and could the widespread backlash have sparked a rethink here? There are suggestions City are reconsidering their membership of the European Super League.
But there has been no comment from the club and it's not clear how they could withdraw now.
What happens on the pitch may be decided in the courts.
The key developments so far
- A dozen clubs - including Arsenal, Chelsea, Liverpool, Manchester City, Manchester United and Tottenham - agree to form a new midweek competition
- European Super League will feature 20 clubs in all and run alongside domestic leagues such as the Premier League
- Founding clubs are being enticed with a share of a 3.5bn euro (£3bn) grant provided by investment bank JP Morgan
- UK government says it is prepared "to put everything on the table to prevent this from happening"
- France's president, Uefa, the Premier League, Europe's major leagues, players' unions and former players strongly criticise the ESL move
- Liverpool manager Jurgen Klopp says he does not agree with the move and that the club's players were not consulted
- A YouGov poll of 1,730 football fans found 79% opposed the idea of a Super League
- The 14 Premier League clubs not involved in the ESL move will meet on Tuesday
- Fans air frustrations on social media and some visit grounds to unfurl banners in protest
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