Khan's lawyer Bawar Awan meanwhile filed a request to Islamabad's High Court seeking protective bail for Khan, which would protect him from being arrested.
Under Pakistan's legal system, police file what is known as a first information report about charges against an accused person to a magistrate judge, who allows the investigation to move forward. Typically, police then arrest and question the accused.
The report against Khan includes testimony from Magistrate Judge Ali Javed, who described being at the Islamabad rally on Saturday and hearing Khan criticize the inspector-general of Pakistan's police and another judge. Khan went on to reportedly say: "You also get ready for it, we will also take action against you. All of you must be ashamed."
Khan could face several years in prison from the new charges, which accuse him of threatening police officers and the judge. However, he's not been detained on other lesser charges levied against him in his recent campaigning against the government.
The Pakistani judiciary also has a history of politicization and taking sides in power struggles between the military, the civilian government and opposition politicians, according to the Washington-based advocacy group Freedom House.
Khan came to power in 2018, promising to break the pattern of family rule in Pakistan. His opponents contend he was elected with help from the powerful military, which has ruled the country for half of its 75-year history.