The Prime Minister vowed to "relentlessly pursue the perpetrators" saying, "They must be brought to justice quickly and be subject to the rule of law that they have sought to subvert."
Dr Singh and Mrs Gandhi visited Saifee and JJ Hospitals where some of those injured are still being treated. (In pics: PM, Sonia visit hospitals in Mumbai)
But their visit is also aimed at checking political criticism. BJP leader LK Advani who visited Mumbai described the three blasts in 12 minutes as "a failure of policy, not intelligence". He said the government needs to set a zero-tolerance policy on terror that extends to dialogue with Pakistan. (Read: Repeated Mumbai attacks prove policy failure, says Advani)
Dr Singh, who has pioneered the resumption of dialogue with Pakistan, will now face many challenging questions in the Monsoon Session of Parliament. Home Minister P Chidambaram was careful to stress that it is inappropriate to speculate on who is responsible for the blasts at Dadar, Opera House and Zaveri Bazaar.
Mr Chidambaram also said that there was no intelligence failure in this case. "Intelligence is collected every day, every hour. It (blasts) is not a failure of intelligence agencies... whoever has perpetrated the attacks has worked in a very clandestine manner", he said. (Read: Not an intelligence failure, says Chidambaram)
For Mumbai, these are finer points that mean very little. All the city seemed to want today was for politicians to stop applying the cliche of Mumbai's "resilient spirit."
A young woman headed this morning to her office said, "We don't expect anything now." (Watch: Stabbed by terror, Mumbai says don't talk of 'resilient spirit')
For a city still recovering from 26/11, the searing attack three years ago in which 166 people were killed, overnight new demons of terror have risen.
A severed head. A heavily-wired dead body that may have been a suicide bomber. And the admission of intelligence sources that whoever is behind the three Wednesday blasts has shown a level of sophistication that's unnerving.
Sources say that the group who engineered the blasts knew better than to communicate via phones or emails. It was familiar with Mumbai's commercial areas and understood how to use the heavy Mumbai monsoon to its advantage. Most security cameras at the locations of the blasts, say Mumbai Police officers, have not revealed clues. Umbrellas conceal many faces caught on camera. A steady drizzle makes it tough to spot anything at all for large parts of the footage. (Watch: Why is Mumbai an easy target?)
Three or four people seen speaking on cellphones for more than an hour near Opera House are being zeroed in on.
These sources point to the likelihood of sleeper cells of the Indian Mujahideen being activated. The indigenous terror group has operated in the past on behalf of Pakistan's Lashkar-e-Taiba (LeT). (Read: Indian Mujahideen sleeper cells may have got activated, says sources)
Sophisticated IEDs, triggered by cellphone alarms
A grainy picture is gradually emerging of how the blasts took place - sophisticated Improvised Explosive Devices (IEDs) were used; they were triggered by alarms set on cellphones. No SIM cards have been found at the locations of the blasts. Two of the bombs used over a kilo of ammonium nitrate. Officers from the National Investigating Agency (NIA) spent all night and much of the day examining the locations of the blasts.
Mr Chidambaram referred this morning to a severed head being found. Union Home Secretary RK Singh said a corpse in JJ Hospital had wires attached to it. He said he could not yet say if this was a suicide bomber, or a victim who was standing so close to the explosion that parts of the explosive clung to him.
The most powerful blast of the three was at Zaveri Bazaar, but the one at Opera House - a hub for diamond traders - had the maximum impact because of the way the explosive was placed. Eleven people were killed and 73 people were injured at this part of South Mumbai. (Watch: At morgues, shattered families claim their own)
As most of Mumbai picked up the pieces to get back to work today, some families spent their hours collecting loved ones from the morgues at hospitals and performing last rites. Faiz, a man in his 70s, buried his young son this evening, who got married just two months ago. "Asghar was my favourite child," he said. "What was my heart's joy has turned into mourning." (Watch: His son, recently married, died at Zaveri Bazaar)
The injured are being treated at KEM (022-24136051), Nair (022-23085379), Harkishandas (022-23855555/30095555), Saifee (022-67570111).
(Watch live video of our complete coverage)