At least three people have been killed and seven others injured in two separate bomb blasts in Somalia’s capital city of Mogadishu.

The first explosion occurred in a busy market on Monday and killed two people.

"It was a bomb they planted in a small room in the market that the local government staff used as they collected tax," said Ahmed Hassan, a local official, referring to al-Shabab fighters who have claimed responsibility for both blasts.

In the second explosion on the same day, a government worker died in hospital due to serious injuries he sustained when a bomb detonated as he was driving his car in Mogadishu, said Ahmed Issack, a police officer in the capital.

According to Issack, it was not immediately clear if the bomb was planted in the car or along the road and detonated remotely.

Somalia has been the scene of clashes between government forces and al-Shabab fighters since 1991.

Al-Shabab fighters have been pushed out of Mogadishu and other major cities in Somalia by the African Union Mission in Somalia (AMISOM), which is made up of troops from Uganda, Burundi, Djibouti, Sierra Leone and Kenya.

In early March, African Union and Somali troops managed to seize the town of Buulobarde from the fighters. Al-Shabab has since stepped up attacks against the troops in the town.

Somalia did not have an effective central government until September 2012, when lawmakers elected Hassan Sheikh Mohamud as the new president.