MQM has submitted the list to the office of Prime Minister Nawaz Sharif, ratcheting up pressure on him to make the force, and the military to which it answers, more accountable.
The MQM has accused the military of illegally detaining members before, as the Rangers pursue a major crackdown on crime in Karachi.
But the list, which Reuters has seen, raises the stakes by documenting dozens of alleged extrajudicial killings.
Neither the Rangers nor the armed forces responded to requests for comment on the list and Karachi operation, launched in late 2013 to tackle soaring crime rates.
Police spokesman Qamar Zaib Satti declined comment, except to say that some cases of alleged extrajudicial killings were being investigated by a directorate set up by the Supreme Court.
Information Minister Pervez Rashid denied the MQM was being singled out.
"The Karachi operation is only targeting criminals and not any particular party," he said.
"The prime minister has formed a grievances redressal committee to address the MQM's concerns. Their reservations are of a political nature and they will be addressed politically."
The committee was formed in August, but has had no reported meetings.
Some senior current and former Karachi police officials have admitted to extrajudicial killings during the operation in Karachi, which the MQM has long been accused of running like a mafia state.
Trading blame
While Karachi murder rates have dropped sharply and many local businesses welcome the Rangers operation, allegations of brutal and illegal methods reinforce the impression of a force acting with impunity.
They have also undermined Sharif, who has struggled to impose his will over the powerful and popular military since coming to power in 2013.
Although nuclear-armed Pakistan has been ruled by the military for half its history, Sharif was elected in the country's first democratic transition of power.
"In all 46 cases, they are either killed in fake encounters (shoot-outs) by Rangers or police or they are picked up by them and we find their bodies dumped somewhere days or weeks later," said senior MQM leader Nadeem Nusrat of the list.
"Petrol, bottles and red hot rods have been inserted in their rectum area. The skin is exposed to acid. Their genital areas have been tortured with electricity. They are shot at close range."
The UN Working Group on Enforced or Involuntary Disappearances referred 35 cases of illegal abductions of MQM workers to the government in May and 20 in August, concluding a "pattern of specific targeting" of the MQM by Rangers.
For their part, law enforcement agencies and many Karachi residents accuse the MQM of racketeering, the abduction, torture and murder of opponents and holding the city to ransom by calling mass strikes at will.
The party denies the charges and says it is being victimised. Some members fear the army's ultimate aim is to weaken the MQM to free space for other, more sympathetic parties in Karachi.
Reuters spoke to the families of several people on MQM's list. Authorities say some victims are killed in gunfights, but relatives believe they were executed.
Despite the accusations, the Rangers have plenty of support in Karachi, home to a deep-water port and vital to the country's economy.
This month, Sharif himself praised the crackdown.
A major textile business owner, declining to be named, said: "I say give Karachi to Rangers for 100 years. At least then we can sleep easy."
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