Muammer Guler, the governor of Istanbul, described the explosions as a "terror attack".
"The blasts occurred in a very busy district and this raised the casualties. Thirteen citizens lost their lives in this heinous attack," he said.
Guler said that that the bombs had been placed in rubbish bins.
"The first explosion was not very strong," Huseyin Senturk, who owns a shoe shop in the area, said. "Several people came to see what was going on. That's when the second explosion occurred and it injured many onlookers."
Recep Tayyip Erdogan, the Turkish prime minister, and Abdullah Gul, the president, strongly condemned Sunday's bombings.
"No goals can be achieved with violence, killing innocent people and terrorism," Gul said in a written statement. "These attacks show how inhumane and miserable the instigators are."
Injured
TV footage showed several wounded people lying on the ground waiting to be treated. Broken glass and debris was strewn all over the area.
"Tens of people were scattered around. People's heads, arms, were flying in the air," one witness told the Reuters news agency.
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The blast occurred in a busy shopping street in the Gungoren district [AFP]
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A nearby hospital said that around 25 people were being treated and three of them were in serious condition.
Guler said that it was too early to speculate who had carried out the attack, but officials will study surveillance cameras from the area to as part of the investigation.
Earlier local media reports had suggested that a gas leak had caused the blasts.
Jody Sabral, a local journalist, told Al Jazeera that a number of groups, including the Kurdistan Workers' Party (PKK) who are vying for a breakaway Kurdish state that would include part of Turkey, could have possibly carried out the attack.
"The PKK, a Kurdish militant group, for example have been known to use packet bombs in civilian areas. And also, more recently, Turkey has been the target of al-Qaeda militants who are known to have cells here, but it is really too early to say right now," she said.
Omer Taspinar, a Turkish expert from the Brookings Institution, said it was likely the PKK were responsible, "but it's not a typical PKK tactic to strike in central Istanbul," he added. "They're much more active in the southeast."
"Two alternatives - One, a shadowy terrorist organisation called the Deep State, with links to higher generals and politicians in the country. They're a right-wing, ultranationalist organisation who may be sending a message to the government.
"The third one, an al-Qaeda-linked organisation."
Explosives
Damla Aras, a Turkish political analyst, said that investigators would be looking into what types of explosives were used.
"There is a possibility they might be A4, C4 explosives, which were brought from northern Iraq by the PKK and have been used several times in Turkey," she said.
In the past, a number of attacks in Istanbul have been blamed on the PKK, which has been fighting since 1984 for independence or greater autonomy for the Kurdish-majority southeast region of the country.
However, Turkey is also in a state of political turmoil, with the ruling AK party facing a potential ban when a court case against it gets under way on Monday and the arrest of dozens of people accused of plotting to destabilise the government.
Earlier this month, three police officers were killed when three armed men jumped out of a car at the US consulate in Istanbul, beginning a gunfight that lasted for seven minutes. The three attackers were also killed in the shootout.