The group calling itself Inquilab (Revolution) made the claim to local reporters in Indian-controlled Kashmir.
Saturday's blasts, apparently timed to target busy evening shopping areas, claimed at least 61 lives and left scores more injured.
"Such attacks will continue until India pulls out all its troops from the state [of Kashmir] and stops inhuman activities in the state," spokesman for the group, Ahmed Yar Gaznavi, was quoted as saying.
The claim has not been verified, and Indian police say they have no record of such a group existing.
State of emergency
As investigators scoured the scenes of the attacks, Prime Minister Manmohan Singh has urged New Delhi residents to remain calm.
Police have declared a state of emergency in the city and closed all markets as a precaution against further attacks.
On Saturday evening Singh was quick to condemn the attacks, describing the bombings as "dastardly acts of terrorism".
"We shall defeat their nefarious designs and will not allow them to succeed. We are resolute in our commitment to fighting terrorism in all forms," he said in a brief television statement on Saturday evening.
Asked who was responsible, he would only say: "There are several clues."
Most of the deaths occurred at the southern Sarojini Nagar market where the blast caused the explosion of a number of gas cylinders used by stall keepers.
There were also fatalities at Paharganj, an area frequented by tourists near Delhi's main railway station.
Family members carry the body
of a victim of the Paharganj blast
A third blast occurred on a bus in New Delhi's Okhla industrial area, police said, although no-one was killed in that explosion.
"The total deaths are 61 and injuries are 188," an Indian Home Ministry official said on Sunday.
But the official said it would be difficult to give an accurate breakdown.
The first explosion hit at 5.45pm (1245 GMT) in New Delhi's main Paharganj market, leaving behind bloodstained streets and mangled stalls of wood and twisted metal. Within minutes came a second explosion at the popular Sarojini Nagar market and then another blast on a bus in the Govindpuri neighbourhood.
Many people were shopping just days before important Muslim and Hindu holidays when the blasts hit.
Indian police have been scouring
the scenes of the blasts for clues
Muslims will celebrate Eid al-Fitr which marks the end of the Muslim fasting month and Hindus will celebrate the festival of Diwali, during which families exchange gifts, light candles and celebrate with fireworks.
Police said they had detained 10 people, three at the railway station and seven more at unspecified locations across the city.
With security forces putting the capital on maximum alert, officials said the toll was expected to rise from the blasts.
Medics say most shrapnel injuries
were caused by flying glass
Shops in the area have been reduced to ruins, and the explosions set off a number of fires that added to the mayhem.At Ram Manohar Lohia Hospital
, Dr SK Sharma, the emergency room chief, said his team had received four victims from the first blast who were dead on arrival at the hospital and "charred beyond recognition". They were treating 30 people injured in the same explosion, he said.
He said that most were suffering from burns and shrapnel injuries caused by flying glass - not the screws or ball bearings sometimes packed into crude bombs.World condemnationPakistan
denounced the attacks as a "criminal act of terrorism" and called on Delhi
to quickly bring the culprits to justice.
Condemnations of the bombings and messages of support for the Indian government have been pouring in from around the world.
UN Secretary-General Kofi Annan also issued a statement saying he was appalled by the bombings with the timing of the attacks to coincide with important holidays adding to the shock.