Home Minister Shivraj Patil said at least 18 people died in five explosions, but some media reports put the death toll as high as 25. Mayor Arti Mehra said at least 61 more suffered wounds.
"It's a very cowardly act of violence," Mehra told reporters near the scene of two of the explosions, in the M-Block market of the upscale Greater Kailash neighborhood. "They want to break the spirit of Delhi. They have tried this in other places before and they have not succeeded and they will not succeed here. They will not scare us."
Just who the attackers are remains unclear.
A number of Indian media outlets received an e-mail sent just before the blasts warning that India was about to receive "the Message of Death."
"In the name of Allah, Indian Mujahideen strikes back once more. ... Do whatever you can. Stop us if you can," said the message.
The Indian Mujahideen was unknown before May, when it claimed responsibility for a series of bombings in the western city of Jaipur that killed 61 people. The group also said it was responsible for July blasts in the state of Gujarat that killed at least 58.
India, a largely Hindu country, has long battled Muslim militant violence in the Himalayan region of Kashmir, the country's only majority Muslim state, but it's not clear if the new group has any ties to Kashmiri separatist movements.
Investigators contend Indian Mujahideen is linked to - or is a front for - a banned extremist group, the Student Islamic Movement of India, which authorities blame for many attacks in recent years. But they have produced so little evidence against the group that some courts have ruled the banning order should be dropped.
While dozens of people have been arrested in recent months, including some identified as ringleaders, India's underfunded and often ill-trained security agencies haven't been able to stop the attacks.
Bombings have occurred with chilling regularity. Since late 2005, nearly 600 people have died in bombings that Indian authorities blame on Islamic militants.
"The sad part is that this is neither the first nor will it be the last" attack, C. Uday Bhaskar, a New Delhi-based defense analyst, said Saturday night. "Clearly the fact that we have not been able to pre-empt these incidents suggests that there has been an inadequacy" on the part of investigators.
U.S. Ambassador David Mulford condemned the attack. "There is no justification for the vicious murder of innocent people. The U.S. stands shoulder to shoulder with India in the fight against terror," he said in a statement.
There was some good news, though, with police defusing at least two unexploded bombs.
One was recovered near India Gate, a colonial-era memorial and one of the country's best-known symbols, according to Joint Commissioner of Police Ajay Kashyap, the Press Trust of India news agency reported. On weekend evenings, the park there is packed with families who flock to picnic, buy ice cream for their children and enjoy the grass and fountains.
The deadliest explosion was believed to be at the Gaffar Market in the Karol Bagh neighborhood, a warren of stores popular among wholesalers and bargain-hunters. A bomb exploded on a street jammed with clothing shops and stores that sell cheap mobile phones. Hours later, a mangled rickshaw stood in front of the shop where the bomb exploded.
Two explosions occurred just 300 yards apart in Connaught Place, the city's central shopping district. The streets quickly emptied of shoppers and filled with screaming police cars, fire engines and ambulances.
One of those bombs went off by a subway station entrance on a major street, and a police officer said it appeared to have been left in a sidewalk garbage bin. He declined to be identified because he was not authorized to speak to the media. The sidewalk was covered with garbage, broken glass and a small pool of blood.
Raju Chohan was walking through the area with a friend when he heard "a deafening sound and there was some sort of smell in the air."
In the minutes after the blast, the street was filled with blood and chaos, as police officers raced to the scene and passers-by helped victims into taxis and rickshaws to get to hospitals. A Hindu holy man clad in orange robes lay face down in the gutter a few feet away, apparently dead. Another man walked away from the scene, helped by other men, his face covered with blood.
A second blast in Connaught Place went off inside a park crowded with families and young people relaxing on the grass.
"Everyone was running every way," said Raj Kumar, 30, a store clerk. "They heard the bomb and they just started running."
Associated Press writer Muneeza Naqvi contributed to this report.