Chief Prosecutor Mats Åhlund decided to proceed with the preliminary investigation against the three members of the far-right party who may face racial agitation charges.
"I want to find out if the situation classifies as a crime," he told the TT news agency.
The video, recorded in 2010 and published by the Swedish tabloid Expressen last week, shows the three politicians employing terms like “whore”, “darkie”, “darkie-lover” in central Stockholm.
Erik Almqvist, the party's former spokesman on economic policy, is also shown having a heated debate with the comedian Soran Ismail, who is of Kurdish descent.
“This is not your country. This is my country,” Almqvist told Ismail.
The comedian was also told "not to fuck with the Swedes".
“To qualify as racial agitation the insult must target a group, for example an ethnic group," the prosecutor said.
"The statement also needs to have reached more than a few people."
The film also shows the trio picking up iron pipes, seemingly to be used against a man they had argued with earlier that night.
The incident earned the trio the nickname Järnrörgänget ("The Iron Pipe Gang") in the Swedish media.
The prosecutor said he wanted more information before determining whether picking up the pipes could classify as a crime. He told TT he would likely make a decision by next week.