Sushil Kumar Shinde, India's home affairs minister, said the central government had warned state governments that such an attack was planned.
"We have had some information for the last two days of such an incident," he said.
Hyderabad, one of India's largest cities and a leading center of the country's burgeoning pharmaceutical and biotechnology industries, has suffered other such attacks in recent years, usually linked to sectarian friction.
The blast sites Thursday - in the Dilsukh Nagar neighbourhood, packed with shops, restaurants, theaters and a huge produce market - were mobbed by protesters, reporters, the curious, and politicians and their large security contingents. Television news footage in the hours afterward showed chaotic scenes, with some investigators trying to find the remains of explosive devices while huge numbers of people jostled for space around them.
Shinde, speaking to journalists in New Delhi, said that the bicycles were 150 meters away from each other and the bombs detonated about 10 minutes apart, killing eight at one site and three at the other. But he warned that the toll could rise, and it did so, with 13 reported dead by midnight.
In a Twitter message, Prime Minister Manmohan Singh said. "This is a dastardly attack, the guilty will not go unpunished."
Officials sought to diminish the chances of the kind of sectarian rioting that has long plagued the country.
Asked in a news conference if he believed that Muslim extremists were to blame for the bicycle blasts, Shinde said: "We have to investigate. We should not come to conclusions immediately."
Singh, in another Twitter message, said, "I appeal to the public to remain calm and maintain peace."
Asaduddin Owaisi, a Muslim member of Parliament from Hyderabad, called the blasts "cowardly."
"I feel that the priority is to maintain peace," he said. "Let us not fall prey to rumours."
The crush of government officials at the blast sites, along with their enormous entourages and their own police squads, was portrayed by newscasters for the television network NDTV as particularly unhelpful.
The money and resources spent on protecting bureaucrats and politicians has become a source of increasing controversy in India, especially in the wake of a highly publicized gang-rape case in December in New Delhi. But Indian politicians, like those elsewhere, often compete with each other to show who is tougher on acts of terrorism and other crimes.
"We've seen political leaders come into the area and hold press conferences," the anchor on NDTV said. "That's the last thing they should be doing."
Kiran Kumar Reddy, the chief minister of Andhra Pradesh state, held a news conference away from the scene Thursday night and asked people to stay away from the blast areas. Renuka Chowdhury, a leader of the Indian National Congress Party, pleaded with other politicians to stay away as well.
"I really wish politicians would recognize this," Chowdhury said.
The bombings in recent years in Hyderabad have often used homemade explosives.
In May 2007, 13 people died after a bomb went off at the Mecca Masjid, including some who were killed in clashes between the police and Muslim protesters afterward.
In August 2007, a pair of synchronized explosions tore through two popular gathering spots in Hyderabad, killing at least 42 and wounding dozens. Police found and defused 19 more bombs in the hours after the blasts, left at bus stops, theatres, pedestrian bridges and intersections.
In New Delhi in September 2011, a briefcase exploded near the high court, killing at least 12 people and injuring scores.