The deaths come as the Iraqi government has cancelled leave for all military officers two days before an expected verdict - and possible death sentence - in the trial of Saddam Hussein, the former Iraqi president.
The bodies were found throughout the capital between 6am on Thursday and 6pm on Friday.
All were dressed in civilian clothes and had been bound at the wrists and ankles, Mohammed Khayon, a Baghdad police lieutenant, said.
They also showed signs of torture. Khayon said the police had no solid information on the victims' identities or their killers.
South of Baghdad, in the town of Kut, police found 13 more bodies on Friday, pulling seven from the Tigris river, while nine more violent deaths were reported across Iraq.
The US military also announced seven further deaths, including four marines killed in combat in the western Al-Anbar province and three soldiers, all of whom died on Thursday, raising the death toll for November to 11.
In a videotape on Friday, Abdul-Qader al-Obeidi, the Iraqi defence minister, issued the order cancelling all military leave and ordering soldiers on holiday back to duty.
The order took effect at noon on Friday.
Many of Saddam Hussein's fellow Sunni Arabs, along with some Shia and Kurds, are predicting a firestorm of violence if the court sentences the ex-president to death, as is widely expected.
Baghdad and two other Iraqi provinces will also be under curfew on Sunday.
Muwaffaq al-Rubaie, Iraq's national security adviser, said: "The government of Iraq will impose curfew on Baghdad, Diyala and Salah al-Din provinces."
Meanwhile John Negroponte, the US national intelligence director, paid a surprise visit to Baghdad, purportedly to discuss recent demands from Nuri Al-Maliki, the Iraqi prime minister, for a swifter transfer of power from US-led forces to the Iraqi military.
Negroponte arrived just four days after Stephen Hadley, the US national security adviser, visited the Iraqi capital for similar talks.
The US military has announced that al-Maliki planned to raise his military force structure by an estimated 18,000 men to a total of about 144,000. Al-Maliki has said that he believes the quicker his forces control the country, the faster violence will diminish.
General George Casey, the most senior US commander in Iraq, said last month that he believed Iraqi forces would be ready to take control of all of the country in 12 to 18 months, with "some level" of American support.