No video evidence has been uncovered of the chanting during last Friday's World Cup qualifier at San Marino, but the FA said on Friday it did not dispute reports highlighting the abuse that led to fans' monitoring group, FARE, reporting England to FIFA.
Some England fans were said to have sung that the Ferdinand brothers, who were not in the squad for the 8-0 win, should be burned on a bonfire.
"We do not want supporters who chant vile or racist abuse following the England team," Club England managing director Adrian Bevington said in a statement. "The FA will continue to work closely with Kick it Out and FARE to ensure we do all we can to eradicate racism from football.
"We fully recognize that we must continue to address any issues that arise involving our own supporters in the same manner we expect other nations to do so."
The FA said it would assist FIFA as the world governing body analyzes the report from FARE.
"While we have no reason to dispute the media reports which are without doubt made for the right reasons of fighting racism, at this time we have not found any recorded evidence of the specific discriminatory chanting referring to Rio and Anton Ferdinand and the vile 'bonfire' song," Bevington said.
"We will of course continue to review all of our recorded footage ... should evidence of any racial chanting be found, we would expect action to be taken against any individuals."
But, if found guilty, the FA itself would face sanctions, including the possibility of England being forced to play a match at Wembley Stadium behind closed doors.
Fans appeared to be abusing Rio Ferdinand because he declined to join the England squad last week after being selected, citing fitness issues, and then provoked criticism by flying to Qatar to appear on television as a pundit for the San Marino game.
The Manchester United defender responded to the abuse for the first time on Friday.
"You expect+accept banter from fans on the terraces as its part of what makes the game great,but racism is not banter,& from ya own fans. WOW," Ferdinand wrote on Twitter.
"Always a small minority who ruin it for others. Let's not jump to conclusions + assume though as it might just have been banter. We'll see after the investigation."
His brother, Anton, has only ever played for England youth teams, but was the victim in a racism case that had implications for Roy Hodgson's senior side.
Chelsea captain John Terry lost the England captaincy after racially abusing Anton Ferdinand during a match at Queens Park Rangers and later quit international football before serving a ban.
"We will continue to take every possible measure to ensure our supporters conduct themselves appropriately, as most have over the past decade," Bevington said.
"However, we will not accept any racist chanting ... we have made significant progress following the hooliganism that blighted the national team in 1998 and 2000. We must continue to maintain this hard work."
The FA statement also urged an end to nationalistic chants against the Irish Republican Army.
"We ... call on those attending England matches at home and abroad to stop the 'No Surrender' chanting during the singing of the national anthem, both before and during games," Bevington said.
Rob Harris can be reached at http://twitter.com/RobHarris