Bulgarian police have identified 15 fans they suspect are responsible for subjecting black England players to racist abuse and arrested six of them.
The nine not arrested are under police investigation, with three wanted.
England's 6-0 Euro 2020 qualifier win over Bulgaria in Sofia was stopped twice in the first half following racist chanting by home supporters.
"We do not tolerate such behaviour," Bulgaria Ministry of the Interior commissioner Georgi Hadzhiev said.
Bulgaria's football chief Borislav Mikhailov resigned on Tuesday.
But Balakov has since posted a statement on Facebook, acknowledging the incidents on Monday and apologising to "English footballers and to all those who felt offended".
"I condemn all forms of racism as an unacceptable behaviour that contradicts normal human relations," he added.
Bulgarian legend Hristo Stoichkov became emotional when he was asked on TV how to prevent a similar occurrence in future. He advocated that "fans are not allowed in the stadium or even [face] heavier punishments".
Apparently referring to the five-year European ban imposed on English club sides after 39 people died at Heysel Stadium before the start of the 1985 European Cup final between Liverpool and Juventus, he added: "Like in England for years - five years without going to stadiums. People don't deserve to suffer."
Meanwhile, the English Football Association and Uefa have condemned the actions of the 'ultras' section of Bulgaria fans, with Aleksander Ceferin, president of the sport's European governing body, calling for "football family and governments" to "wage war on the racists".
The FA has also offered full support to England players following the racist chanting, with counselling one of the options open to them.
'Stewards joined those chanting'
According to European anti-discrimination body Fare, about 20 stewards joined those involved in racist abuse and far-right activity after taking their hi-vis jackets off.
The European anti-discrimination body had spotters in the crowd and have included their findings in the report they have handed to Uefa.
Fare executive director Piara Powar said: "It is common practice in Eastern Europe. They use security from fan groups as they know their own people. That's the idea but it's not the idea to take off bibs and join in.
"There in lies the problem in some countries. Some of the policing is not fit for purpose.
"We have called for Uefa to kick Bulgaria out of the competition."
Players condemn abuse
England midfielder Jordan Henderson called the behaviour of Bulgaria fans "disgusting", after they were warned for making Nazi salutes and monkey noises.
Henderson added: "I obviously wasn't happy with the situation that we were in - it wasn't nice to be involved in and it shouldn't be happening in 2019."
Team-mate Tyrone Mings, who was making his international debut on Monday, said he heard racist chanting "clear as day" during the pre-match warm-up in Sofia.
A number of players posted on social media following the game, thanking travelling fans for their support and expressing their pride in the performance despite the abuse.
"Not an easy situation to play in and not one which should be happening in 2019," said striker Marcus Rashford. "Proud we rose above it to take three points but this needs stamping out.