The blasts occurred in Aziz Abad area of Karachi and near the office of the Mutahida Qaumi Movement (MQM) close to the central headquarters of the party.
Police and Rescue officials said that the blasts had left four people dead and around 30 were injured who were being rushed to hospital.
"The intensity of the first blast was stronger than the second one which took place few minutes later," SSP Imran Shaukat said.
This is the sixth time in the last two weeks that bomb attacks have been carried out close to MQM election/sector offices in Pakistan's biggest city.
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The explosions were heard from far distances and spread fear among the local residents. Nearby buildings and vehicle were damaged while power outage was also reported in the area after the incident.
Speaking to a private TV channel, MQM leader Wasay Jalil said the explosions occurred near the party's sector office in Azizabad locality. He said several party activists are among the injured.
Tehrik-i-Taliban Pakistan (TTP) spokesman Ehsanullah Ehsan said the target was MQM and both bombings were carried out through planted devices.
"The Saturday's attacks are the continuation of our target attacks on the MQM, PPP and ANP," the TTP spokesman said.
Prime Minister Mir Hazar Khan Khoso has strongly condemned incident.
The Prime Minister directed the concerned authorities to beef up the security measures in order to protect the political leaders, candidates, rallies and the masses.
The Pakistani Taliban have vowed to target secular parties like the Pakistan People's Party, Awami National Party and MQM ahead of the May 11 polls.