The government have vowed to intervene ” if football authorities fail to deal with racism.
Play was stopped during Chelsea’s win at Tottenham on Sunday after Antonio Rudiger said he heard monkey noises.
The Professional Footballers’ Association has called for a government inquiry following the alleged abuse.
“Racism of any kind has no place in football or anywhere else and we must confront this vile behaviour,” said a Downing Street spokesperson.
“Clearly there remains more work to be done by the football authorities in tackling this issue and we are committed to working with them on this to stamp it out.
“The FA, Premier League and English Football League have significantly stepped up their efforts, but we expect them to continue to prioritise this issue and to consult with both players and supporter groups, and we will be monitoring how the football authorities implement their plans through the season.
“We will continue working with the authorities on this, including the Professional Footballers’ Association and we don’t rule out taking further steps if required.”
Tottenham, who have been working with the Metropolitan Police to investigate what happened on Sunday, have promised to “take the strongest possible action” against anyone guilty of racist behaviour.
Spurs say their initial findings regarding the alleged racist abuse of Rudiger are “inconclusive”.
Meanwhile, a Chelsea fan has been arrested for allegedly abusing Son Heung-min.
Sports minister Nigel Adams said he had held positive talks with Tottenham, the Premier League and the PFA, adding: “I am in no doubt that Tottenham are doing all they can to identify anyone responsible, and that they will take the strongest possible action.”
Chelsea centre-back Rudiger reported the alleged racist abuse from the crowd to his captain Cesar Azpilicueta, who told referee Anthony Taylor and the game was stopped.
Shortly after the stoppage, an announcement made over the public address system warned that “racist behaviour is interfering with the game”.
Second and third addresses followed with the game heading towards its conclusion.