Spartak Moscow players described as "chocolates melting in the sun" by the Russian team's Twitter account have said "there is no racism" at the club.
The post accompanied a video, filmed by defender Georgi Dzhikiya, that showed three black players training in sunny conditions. It has since been deleted.
In a new video message, Brazilian striker Luiz Adriano said Dzhikiya was "my brother" and "a club legend".
He added: "I love you my friend. There's no racism at Spartak."
Dzhikiya said: "There is no racism in our team, we are all brothers, we're one big family."
Midfielder Fernando and winger Pedro Rocha - the other two players refered to as "chocolates" - also appeared smiling alongside Dzhikiya, who kisses Adriano on the cheek. They repeat the message that "there is no racism at Spartak".
Fifa said it "condemns the message published on the Twitter account of Spartak Moscow".
"As said many times, any form of discrimination on or outside the field is unacceptable and has no place in football," world football's governing body added.
Russia is scheduled to host the 2018 World Cup this summer.
"As to the handling of this matter, this falls under the responsibility of the relevant national body," Fifa's statement added.
Anti-discriminatory bodies Fare and Kick It Out have also criticised the original tweet.
"Racism is one of the biggest issues Russia faces in the year they host the World Cup. References like this show how some minorities are seen by some in the country," said Fare chief Piara Powar.
In September, Liverpool's Nigeria-born attacker Bobby Adekanye was subjected to racist chants and gestures from Spartak supporters in Moscow during a Uefa Youth League game.
European football's governing body Uefa charged Spartak, who had to partially close their academy stadium for their next Uefa Youth League fixture, leaving 500 seats empty.
Spartak defender Leonid Mironov has also been charged with racially abusing Liverpool striker Rhian Brewster.
The alleged incident took place during a Uefa Youth League game at Prenton Park, which Liverpool won 2-0 in December.
Uefa said the case will be dealt with by its control, ethics and disciplinary body, with a date for the hearing yet to be confirmed.