The UK government has threatened social media companies with "large fines" which could amount to "billions of pounds" if they fail to tackle abuse on their platforms.
It follows a spate of incidents of racism directed at footballers playing in the English leagues.
Culture Secretary Oliver Dowden also said "criminal sanctions" could be considered for senior management.
"We are willing to take the harder, legislative measures," he said.
Dowden was speaking after Southampton's Alex Jankewitz had become the latest footballer to receive racist abuse on social media, with his club contacting Hampshire Police over messages sent to the teenage midfielder.
"It's just pretty outrageous in this day and age" said Dowden, who hosted a meeting with past and present players about the issue last month.
"There's still problems in stadiums but, to a large extent it's not the problem that it was. But it's still rampant on social media."
In a wide-ranging interview with BBC sports editor Dan Roan, Dowden also gave his views on the ongoing studies into sport and dementia, and fans returning to sports venues after the Covid-19 pandemic.
'We'll take the power to impose very large fines'
In recent days, several incidents of abuse directed at football players have once again highlighted the problem of racism on social media.
Former Arsenal and England striker Ian Wright said the authorities and social media companies need to do more to identify the perpetrators.
- Is football's racism battle being lost on social media?
- Rashford racially abused on social media
- Is ending anonymity on social media the answer?
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% of global turnover.
"For some of these big tech firms that's running to billions of pounds."
He added: "As an ultimate pullback, I really don't want to have to do this, but we do reserve the right to criminal sanctions for senior management as well, in the most egregious cases."
No legislation on sports and dementia on the horizon
Dowden said the government currently has no plans to introduce legislation outlining how governing bodies need to act over possible links with their sports to dementia cases among athletes.
"I hope we can bring people together," he said. "I'll have a follow-up session in a couple of weeks with governing bodies, starting with education and awareness, improving their protocols."
- Dementia in rugby: RFU chief accepts language shift needed
- Dementia in football: PFA to create taskforce
On the return of fans to sporting venues
Supporters have been banned from sporting arenas in England since last March because of the pandemic, except for periods in the second half of the year when some were permitted.
Dowden said any reintroduction would depend on the government's plans regarding the country coming out of lockdown.
"I have to say there's a long path ahead of us," he said.
"In the next couple of weeks we'll be engaging with the prime minister and cabinet office as we seek to draw out the map on reopening different sectors. As part of the mid-February announcement, we'll be able to start giving some indication as to what that path will look like.
"I'm very optimistic in the medium-to-long run, but I do think we need to progress with caution in the short run."
- The Monday Night Club: How has Pep turned things round and can Micah get Timo Werner firing?
- Hip Hop that shook America: How Kanye West challenged ideas about rap and religion