The woman, aged between 18-20, might have been killed by her estranged lover, said an investigation team officer, who did not wish to be named.
The officer told IANS that they were trying to identify the victim.
"An old wound mark was found on the victim's thigh but it was not enough to identity her," said the officer.
"The legs of the woman were found from a canal in west Delhi's Sagarpur area around 8.30 a.m. Friday while the trunk of the victim was recovered a few metres away after an extensive search," Additional Commissioner of Police A.K. Ojha told IANS.
It seems the body of the woman was chopped into pieces after killing her at another place, Ojha said.