Coca-Cola has called on Fifa to undergo an immediate, independent reform process led by an external figure in what amounts to the most significant challenge to date by one of the embattled governing body’s corporate backers.

The soft drinks giant, a World Cup sponsor since 1978, has confirmed in a letter to the International Trade Union Confederation that it wrote to Fifa last week calling for an independent commission to undertake root-and-branch reform led by “one or more eminent, impartial leaders”.

That would amount to a call on the Fifa president, Sepp Blatter, to allow an independent, well-respected figure from business or politics to oversee a wholesale reform of its structure and governance.

Coca-Cola, which could potentially consider walking away from Fifa if its requests are not met, said in the letter – seen by the Guardian – that such an action would be the only way “to manage the efforts necessary to help reform Fifa’s governance and its human rights requirements”.

Although some of Fifa’s sponsors, who collectively contribute more than $1.5bn (£960m) over each four-year World Cup cycle, have previously called on Fifa to restore its credibility Coca-Cola has become the first to advocate wholesale reform.

The letter follows a campaign by a coalition of bodies including the ITUC and the sportswear brand Skins under the New Fifa Now banner to try to force sponsors to take responsibility for driving change at Fifa.

The campaign has intensified in the wake of the recent meltdown that followed the indictment of 14 football executives by the US department of justice on corruption charges.

The ITUC general secretary Sharan Burrow said Coca-Cola had set a benchmark and called on other sponsors to follow suit. She said: “It’s now time for the other sponsors such as Visa, Adidas and McDonald’s to take a stand against corruption and put the game back on track.

“Football and other sports carry the passions of billions around the world, can effect real change and solidarity and corruption has no place in this. We back the leadership of Coca-Cola and call on the Fifa executive to do the right thing on Monday.”

“An external reform commission led by a man like Kofi Annan supported by men and women including sports leaders and players with similar integrity can make the difference.”

Jaimie Fuller, the head of Skins, said: “Coca-Cola are to be applauded for having the courage to take an ethical stance on something that is so commercially sensitive. It’s great that Coke understand and respect the power of sport in society and the good that it can do in the right hands. This is the reverse of the culture within Fifa and Coke’s demand for independent reform is a reflection of true leadership.”

After the Guardian revealed that Coca-Cola had made its intervention, McDonald’s also confirmed that it had written to Fifa demanding fundamental reform. Both companies have their global headquarters in the US, which has been the driving force behind the criminal investigation into Fifa executives.

A spokeswoman said: “At McDonald’s, we know our customers around the world are passionate about football, and we share their enthusiasm. That’s why we’ve sponsored the World Cup globally for more than 20 years. But recent allegations and indictments have severely tarnished Fifa in a way that strikes at the very heart of our sponsorship.”

“As a result, we have expressed our concerns directly to Fifa. We believe Fifa internal controls and compliance culture are inconsistent with expectations McDonald’s has for its business partners throughout the world. We are not satisfied with Fifa’s current handling of the recent incidents that go clearly against McDonald’s culture and values. Fifa must now implement meaningful changes to restore trust and credibility with fans and sponsors alike.”

Coca-Cola, which has a contract until 2022, is believed to have been among the sponsors that contacted Fifa in the wake of Blatter’s re-election, which came days after seven Fifa executives were arrested in dawn raids in Zurich.

Three days after his re-election Blatter promised to stand down at a special congress, expected to be in December. The date will be decided at an executive committee meeting on Monday at which Blatter is expected to bring forward his own suggestions for reform. But many campaigners, including the anti-corruption watchdog Transparency International, believe that it is only through an independent reform process overseen by an external figure that Fifa can regain its credibility.

In a manifesto for change published earlier this week, Transparency International also called for an independent commission to overhaul Fifa, term limits for executive committee members, transparency on pay and bonuses, the introduction of independent directors and for personal bribery to be further incorporated into Swiss criminal law.