At least 58 people were killed and many more wounded in the blasts on Saturday, officials said.
Police declared a state of emergency and ordered all the markets in New Delhi closed.
While urging people to remain calm, Prime Minister Manmohan Singh denounced the apparently coordinated bombings as terrorist attacks.
"India will win the battle against terrorism," Singh said in a statement, according to one of his top advisers, Sanjaya Baru.
He did not say who was suspected in the explosions, but it is known that the Indian government faces opposition from dozens of militant organisations, including Kashmiri separatists and those opposed to the peace process between Pakistan and India.
Officials did not name any
suspects in the blasts
The first blast took place at about 5.45pm in the central Paharganj market, which was crowded with shoppers ahead of Tuesday's Diwali festival, a Hindu holiday where families gather to exchange gifts, light candles and celebrate with fireworks. Minutes later, two more blasts exploded at the Sarojini Nagar market and on a bus.
"When I got up, there were people everywhere - they were bleeding and screaming," said shop owner Anil Gupta about 45 minutes after the blast as he sifted through the wreckage of his jewellery store. Scattered around his feet were bracelets, necklaces and earrings.
Home Minister Shivraj Patil urged people to stay off the streets. "I appeal to you. Please disperse from the markets and go back to your families," he said in a televised address.
Patil said 39 people were killed in the blast at the Sarojini Nagar market in the south Delhi.
Sham Lal, an official with the Delhi fire department, said at least 16 people died in the Paharganj market blast, and another three were killed on a bus in the Govindpuri neighbourhood. He had no further details.
An orderly attends to a man
at Ram Manohar Lohia Hospital
The explosions also come as India and Pakistan began talks on opening their heavily militarised frontier in disputed Kashmir to bring food, shelter and medical aid to victims of the Himalayan region's massive earthquake, which killed about 80,000 people, most of them in Pakistan.
Pakistan condemned the attacks, calling them "barbaric" and a "criminal act of terrorism".
Witnesses said the blasts rocked neighbourhoods.
Babu Lal Khandelwal, a shop owner in the Paharganj market, an area near the city's main train station and packed with small shops and inexpensive hotels often filled with foreign backpackers, said the blast knocked him to the ground.
"There was black smoke everywhere. When the smoke was cleared and I could see, there were people bloody and people lying in the street," Khandelwal said.
The blast occurred in a small square of the market and badly damaged a row of shops, including Khandelwal's clothing store, Hirasons.
India and Pakistan began talks
on aiding the earthquake victims
About an hour after the explosion, investigators stood around a small crater filled with debris about 3m from the group of shops.
Broken glass and other debris littered the street, shop signs were ripped and twisted and clothes - mostly T-shirts and scarves - hung from low-strung power lines.
The second blast targeted the market in Sarojini Nagar, a popular shopping district in the southern part of the city offering everything from knockoff designer clothing to kitchen crockery.
Govind Singh, who sells wallets and toys on a cart next to a juice shop devastated in the explosion, said at least five people from his village died in the blast.
The explosion was "so loud that I fell down. Then a fire started," he said.
"India will win the battle against terrorism"
Prime Minister Manmohan Singh
"I took out at least 20 bodies; most of them were children," Singh said. He and others wrapped the bodies in sheets that were being sold by one of the destroyed shops.
As he spoke, someone asked him: "Where is Lal Chand?"
"He is gone," Singh replied before he started crying.
At Ram Manohar Lohia Hospital, Dr SK Sharma, the emergency room chief, said four victims of the first blast were dead on arrival and "charred beyond recognition".
They were treating 30 injured from the same explosion, he said.
Police gather at the site in the
Paharganj market in New Delhi
However, the burns were not caused by chemicals and most shrapnel injuries had come from flying glass - not the screws or ball bearings sometimes packed into crude bombs, Sharma said.
"Those who were nearby, they got burn injuries; those who were just nearby got burn and splinter injuries," he said.
As he spoke, an ambulance pulled up and paramedics wheeled more victims into the hospital.