The prime minister said FIFA should sort its own affairs out rather than interfere in tributes to a country's war dead.
While FIFA maintained its rejection, the prime minister said FIFA should sort its own affairs out rather than interfere in tributes to a country's war dead.
"It is utterly outrageous," May said when asked about the matter in parliament.
"Our football players want to recognise those who gave their lives for our security.
"It is absolutely right that they should be able to do so.
"A clear message is going from this house before they (FIFA) start telling us what to do they jolly well ought to sort their own house out."
FIFA was linked with scandal that led to its president Sepp Blatter being ousted in December. A new regime is now in place.
The English and Scottish football associations have been negotiating with the world body, which bans political, commercial and religious symbols on team outfits during matches. A FIFA statement issued Wednesday reiterated the stance.
"FIFA fully respects the significance of commemorating Remembrance Day on November 11 each year," it said.
"The laws of the game are overseen by the International Football Association Board (composed of the four British FAs and FIFA) and applicable to all 211 member associations.
"The relevant Law 4, para. 4, clearly states that the players equipment should not carry any political, religious or commercial messages.
"The laws are applied uniformly in the event of similar requests by any member association to commemorate similar historical events."
However, FA chairman Greg Clarke -- whom it is believed will meet with FIFA secretary-general Fatma Samoura in London later Wednesday -- said it was inconceivable poppies would not be worn.
"My personal opinion and actually the same opinion I hold as Chair of the FA is of course we should wear poppies," he told ITV.
"We are commemorating millions of people who gave their lives in wars over the last hundred years and they deserve that.
"The people who lost relatives deserve that. That?s our plan.
?We'll be wearing poppies at Wembley.
"We're negotiating in good faith with FIFA to try and find a solution. But there will be poppies at Wembley."
England play Scotland in a World Cup qualifier at Wembley on November 11, the day when Britain traditionally remembers its war dead.
Many Britons wear red poppies as a tribute to those who have died in conflicts which have involved the country.
In 2011, FIFA agreed to let England wear a poppy symbol on black armbands when they played Spain in a friendly on November 11.
The strength of feeling against FIFA was reflected when by Wednesday nearly 200,000 people had signed a petition urging a rethink.
The petition was launched by former RAF navigator John Nichol -- who was shot down with pilot John Peters and taken prisoner during the first Gulf War with Iraq in 1991.
"The poppy is not a political statement at all. It could not be further from a political statement," said Nichol, who along with Peters was tortured while being held prisoner.
Conservative lawmaker Damian Collins, chairman of the Commons Culture, Media and Sports Committee, told the BBC FIFA were playing a double game where the rule was good for one but not for another.
"Someone has shared with me on social media an Ireland football shirt that has a special embroidery on marking the centenary of the Easter Rising," said the 42-year-old, a co-founder of 'New FIFA Now' group campaigning for reform of the world body.
"FIFA allow that, so I think people will find it astonishing that the poppy's not allowed."