The mass slaying of women is unusual in Mexico's drug war, and there was no indication the cases in the two cities were related.
Residents of the capital's tree-lined San Miguel Chapultepec neighborhood discovered the woman's upper body on one block and her left leg and right leg on two other blocks, the city prosecutor's office said Saturday. The fingers of her left hand had been cut off.
The prosecutors' office provided no details on the woman's identity or a possible motive for the killing. Officials did not return requests for comment Sunday.
Mexico City has been somewhat of an oasis from the cartel violence engulfing border states, but a spate of recent killings and decapitations has residents fearing the drug war is encroaching.
In Acapulco, police said they were not ruling out drug or organized crime links possibly related to prostitution in the killings of four women and a 14-year-old girl whose bodies were found Saturday.
All five worked at a beauty parlor in a neighborhood known for prostitution and drug dealing, the chief of detectives for the Guerrero state police told The Associated Press on Sunday.
"It's an area with many social problems," Fernando Monreal Leyva said.
"On the second floor where the events occurred - in this case, the beauty parlor - a massage parlor was found where sexual acts may have been performed, although this is still under investigation," Monreal Leyva said.
The teenage girl had begun working at the salon five days prior to her death, he added.
Three of the bodies were found at the salon located outside the tourist district. They had been stripped of their clothes and their hands and feet were tied, police said.
The other two victims were found separately in other parts of Acapulco - one in an abandoned car and the other on a street behind a church. All of the women were 30 years old or younger.
Police had no suspects or motives and were trying to determine whether all of the women were killed at the same spot, Monreal Leyva said.
Guerrero state has seen a spike in violence since rival factions of the Beltran Leyva cartel began fighting over territory following the December 2009 death of capo Arturo Beltran Leyva in a gunbattle with Mexican marines.
Farther north on Mexico's Pacific coast, a young man was shot to death in the lobby of a luxury hotel Saturday in Cabo San Lucas, the Baja California Sur state prosecutor's office said. State police said the man was hit by seven bullets in his back and head, but did not provide details of a possible motive for the killing.
It was unclear if the killing was drug-related. Drug gang violence - which has claimed more than 34,600 lives in Mexico over the past four years - has been extremely rare in Cabo San Lucas, a resort dotted-area at the southern tip of the Baja California peninsula.
Associated Press writers Sergio Flores in Acapulco and Ignacio Martinez in Cabo San Lucas contributed to this report.