Police said that 32 officers had been injured during and after crowd trouble at the Georgi Asparuhov stadium, home of CSKA's bitter rivals Levski .
"We'll not succumb to such provocations," Sofia police's chief Valeri Yordanov told a news conference on Sunday.
"CSKA fans' actions were pre-staged, some of them began break off concrete and iron pieces immediately after arriving at the stadium."
CSKA fans broke the safety fences and pelted police with fireworks and other objects during the first half of the match which CSKA won 3-1.
In response, hundreds of policemen, wearing helmets and using batons, stormed the CSKA supporters' section and forced them outside the ground.
Yordanov said that the fans' aggressive behavior and the possibility of pitch invasion prompted police to move in and charge the supporters with batons.
He also blamed the fans of violating a prior agreement between the two sides and police.
Nearly 1,500 policemen were on duty for the "eternal derby", as matches between Levski and CSKA are known in the Balkan country.
Police also used horses, dogs and specialised equipment to tackle public order offence.
Sofia police said earlier this week they met with the Bulgarian Football Union (BFU) officials and suggested an earlier kick-off to prevent the game ending in the dark but the soccer authorities did not comply with the request.
"It was really serious, 32 policemen were injured during and after the match," said Yordanov, adding that police arrested 23 fans on Saturday but the number will increase as some of the offenders will be identified from video footage.
The fixture has a long history of crowd violence. A 30-year-old man was killed by a bomb in 2000 and hooliganism and arrests have been rife since.
CSKA fans accused the police of "exceeding their rights" and said they wanted a meeting with Bulgaria's Interior Minister Tsvetan Tsvetanov to discuss the incidents.
"We respect the law and the Bulgarian police but it's not acceptable for 3,500 fans to be pushed outside the stadium because of the misconduct of two or three," CSKA's national fan club chairman Dimitar Angelov said.
Sofia municipality said on Sunday that the BFU should introduce lunchtime kick-offs for matches between Levski and CSKA - the most popular clubs in the country.
"I think this will limit the possibility of clashes and police will have better chance to cope with the situation," said Sofia deputy mayor Ivan Sotirov.
