Arsenal chief executive Vinai Venkatesham said this week that abuse endured by black players on social media sites is the "biggest problem" in football.
On Friday, Arsenal winger Willian called for change after revealing he was called a "monkey" by two different Instagram users after Arsenal's 1-1 UEFA Europa League draw against Benfica.
Willian's Arsenal team-mate Eddie Nketiah, Manchester United's Marcus Rashford and Anthony Martial and Chelsea's Reece James are among the others to have suffered racist abuse on social media.
A number of the abusive messages have come from accounts where an individual hides behind a pseudonym, and it has been repeatedly mentioned within football that social media companies should prevent anonymous users.
Defending its policy, a Twitter statement read: "At Twitter, we are guided by our values, and never more so than when it comes to fundamental issues like identity.
"We believe everyone has the right to share their voice without requiring a government ID to do so.
"Pseudonymity has been a vital tool for speaking out in oppressive regimes, it is no less critical in democratic societies."
The American company did promise to work alongside the UK Government and football authorities, including anti-racism group Kick It Out, to fight the issue.
"We join our partners in condemning racism and we will continue to play our part in tackling this unacceptable behaviour – both online and offline. We want to reiterate – there is no room for racist abuse on Twitter," the statement added.