Singh said he understood the "shock and outrage of the people" of Mumbai over Wednesday`s bombings, which marked the deadliest attack in the city since the 2008 siege by Islamist militants in which 166 people died.
"Perpetrators of the Mumbai blasts shall be pursued relentlessly and brought to justice quickly," Singh said after flying in to India`s financial capital.
"I understand the shock and outrage of the people of Mumbai, I share their pain, anguish and anger."
The strongest of the three coordinated explosions hit a busy jewellery trading area in the south of the city, the same district targeted in the 2008 assault blamed on the Pakistan-based Lashkar-e-Taiba militant group.
The memory of that attack -- 60 hours of mayhem as 10 gunmen rampaged through the main railway station and luxury hotels -- is still fresh in the minds of city residents.
Singh`s statements came as Indian investigators turned to CCTV footage in their struggle to identify who was behind Wednesday`s evening rush-hour blasts.
Earlier on Thursday, Home Minister P. Chidambaram, who also visited Mumbai, said there had been no intelligence warnings of an impending attack.
"All groups hostile to India are on the radar. We are not ruling out anything, we are not ruling in anything. We are looking at everyone," he said after visiting the scene of the three blasts.
The Home Ministry said police were interrogating suspected members of a homegrown militant group, Indian Mujahideen, who had been arrested in Mumbai several days ago in connection with bomb blasts in the western state of Gujarat in 2008.
The blasts came before a visit to India by US Secretary of State Hillary Clinton next Tuesday and ahead of peace talks between the Indian and Pakistani foreign ministers that are slated for New Delhi in the last week of July.
India`s foreign ministry spokesman said the talks would go ahead. (*)
Editor: Kunto Wibisono
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