At least 33 people have been killed in religious rioting in Orissa since Saraswati's murder.
The Maoists said they killed Saraswati because he was forcing tribal people to reconvert to Hinduism.
"We ordered the death penalty for him," Sabyasachi Panda, the Maoist leader, said.
Claim disputed
Panda said his group had left letters at the site of the killing claiming responsibility but that local authorities had hidden the evidence.
"The state government made it look like Christian groups are responsible for the attack," Panda was quoted by the NDTV as saying.
But Hindu hardline groups led by the Viswa Hindu Parishad (VHP) have rejected the Maoist claim, saying the murder of a Hindu religious leader did not serve the Maoist agenda.
"Have the Maoists started fighting in the name of God now," Subhas Chauhan, a senior VHP leader, was quoted by the CNN-IBN television station as saying.
Chauhan and his supporters say Saraswati opposed conversions to Christianity and his elimination can only benefit the Christian missionaries active in the area.
Saraswati's killing prompted clashes across the state, with tens of thousands of people forced from their homes after Hindu groups attacked churches and the homes of some Christians.
Hindu villagers at some places have also allegedly come under attack from Christian hardliners.
On Friday, the Orissa government said police had arrested four people for the alleged rape of a nun during the riots.
Communal violence
Hindu groups, including Bajrang Dal, a Hindu youth movement that seeks to promote respect for the Hindu religion, have accused Christian missionaries of bribing poor and low-caste Hindus to convert to Christianity by offering free education and health care.
But Bajrang Dal has come under scrutiny in Karnataka, a state in India's south, where religious violence has also flared up in recent weeks.
The National Commission for Minorities, which visited sites in Karnataka where Christians were said to have been attacked, has suggested a ban on such organisations, saying they are "responsible for breakdown of communal harmony".
The Commission's report said authorities in Bangalore, capital of Karnataka, reported that of 93 people in custody in connection with the violence, 36 of them were members of Bajrang Dal.
"The reasons for the violence in Orissa and Karnataka seem to be different," Valerian Rodrigues, a professor at the Centre for Political Studies at Jawaharlal Nehru University, told Al Jazeera
"In Orissa, the major confrontation is between scheduled caste Christians - normally called Dalit Christians - and tribal groups largely organised by Hindu nationalist groupings, particularly the extreme side of it called the Bajaran Dals," he said.
"But in Karnataka, the Christians have been present there for the last 400 years and it is surprisingly for the first time the Catholic church - which is the predominant presence of Christians there - that has been targeted."