The Movement for Rights and Freedoms (MRF) accused the police and security services of failing to protect Ahmed Dogan from the man who tried on Saturday to shoot him twice before being wrestled to the ground by security guards.
"The main goal of the investigation would be to focus on finding out who was the political mastermind of this attack," said Lyutvi Mestan, who replaced Dogan as MRF party leader as previously expected on Saturday.
"The authorities are working on the lead that this was an individual action of a criminal .... this is a huge stain on Bulgaria's image," he told a news conference.
The party called for an international investigation into the assault by the 25-year-old man, who police identified as Oktay Enimehmedov, an ethnic Turk from the Black Sea town of Burgas.
Police said the gun used during the attack was a non-lethal gas pistol and deputy chief prosecutor Borislav Sarafov told reporters Enimehmedov faces up to five years in prison for hooliganism and up to six years for making a death threat.
Political parties in Bulgaria strongly condemned the attack against Dogan, one the most influential political figures in the European Union's poorest member.
"The attack against Dogan is not a hooliganism. This is an assault against the national security. I categorically reject any claims that the incident was staged," said Bulgarian Socialist Party leader Sergei Stanishev.
Prime Minister Boiko Borisov told reporters: "This is a very disturbing event and should not happen in today's Bulgaria."
The liberal MRF party represents ethnic Turks and other Muslims who make up about 12 percent of the Balkan country's population of 7.3 million. Dogan was named honorary chairman on Saturday of the party he has led for 23 years.
Most Muslims in Bulgaria are not recent immigrants but are a centuries-old community, mostly ethnic Turkish descendants of Ottoman rule.
The MRF was a junior partner in the previous Socialist-led cabinet in Bulgaria, which is due to hold parliamentary elections in July.
(Reporting by Angel Krasimirov; Editing by Sophie Hares)