Social media companies face "large fines" which could total "billions of pounds" from the UK government if they fail tackle abuse on their platforms.
England internationals Marcus Rashford and Reece James are among a number of footballers to have been subjected to racism in recent weeks.
Individuals and clubs, as well as the Football Association and Premier League, have condemned the abuse and called on social media firms to take tougher action against hateful messages.
"We are willing to take the harder, legislative measures," Culture Secretary Oliver Dowden told the BBC.
Southampton's Alex Jankewitz became the latest footballer to receive racist abuse on social media, with the Premier League club contacting Hampshire Police over messages sent to the 19-year-old midfielder.
Dowden said: "I certainly am prepared to get tough.
"If you fail to enforce your own terms and conditions, stand up to your duty of care, then we will impose fines and we'll take the power to impose very large fines - indeed up to 10 per cent of global turnover.
"For some of these big tech firms that's running to billions of pounds."
Kick it Out said a collective effort was required to "change the culture of impunity" with online abuse and insisted "social media companies have to step up and play their part in pursuing offenders and wiping out online abuse for good".
"We support the government stance on tackling online hate," a statement added.
"We want to see change on the social media platforms implemented as quickly and comprehensively as possible. Too many footballers have experienced abuse on their social channels for too long. Change has to come now."
Dowden added senior management at social media companies could face "criminal sanctions" in the "most egregious cases".
Social media companies have reiterated their commitments to eradicating online hate and earlier this month Instagram's owner Facebook removed a user who racially abused Brentford forward Ivan Toney.
Townsend: Conversations have gone on too long - time for action
Troy Townsend, head of development at Kick It Out, said football players a fed up with conversations taking place over social media abuse and that closing accounts was not a tough enough measure.
Ian Wright said he was "disappointed" after a teenager who sent the former England striker racist abuse was not given a criminal conviction and Townsend added his reaction to messages of hate had "gone beyond frustration".
Speaking to Sky Sports News, Townsend said: "I was involved in conversations [with Twitter 18 months ago] but those conversations are still happening and what status are they at.
"The players are not interested in conversations anymore. They share their experiences; it is in the public domain, It is easily accessible if you want to see it. It is now about the action, the appropriate action and that appropriate action is not just closing down an account and saying that person is no longer able to use our platform because that person has probably gone and opened another account anyway."
He added: "Now is the time for the biggest voices, the most powerful voices to be talking out and reaching out to those social media companies and almost warning them that this cannot continue or else and I think that is the stage we are at now."
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