In a televised speech Wednesday, Khan said he was angry about a speech given hours earlier by cleric Afzal Qadri who told a rally in Lahore that the judges who acquitted Asia Bibi deserved to be killed under Islamic law. Qadri made his speech hours after Asia Bibi was acquitted.
Khan said the cleric also incited people to oust his government and troops to revolt against the country's army chief Gen. Qamar Javed Bajwa. He said "the state will fulfill its responsibility" and asked the Islamists not to compel the state to take action against them.
Pakistan's top court has acquitted a Christian woman who has been on death row since 2010 for insulting Islam's Prophet Muhammad.
In Wednesday's verdict, the court ordered authorities to free Asia Bibi.
Bibi was being held at an undisclosed jail for security reasons.
The landmark ruling is expected to anger Islamists who had threatened to launch nationwide protests if the court freed her.
Bibi was arrested in 2009 after a quarrel with Muslim women.
Islamists have demanded her execution. A governor and a minister of minorities were assassinated in 2011 for supporting her.
Insulting Islam is punishable by death in Pakistan, and the mere rumor of blasphemy can ignite lynchings.