shops, offices and schools were shut amid tensions over the disappearance of an opposition leader.
There was no damage or injuries from the explosions but one opposition supporter was shot dead elsewhere in clashes with ruling party activists late on Saturday, police said.
Two of the nine homemade bombs were hurled at the Secretariat, home to several government ministries and offices, deputy commissioner of police Syed Nurul Islam told AFP.
"Two unidentified youths drove motorbikes outside the Secretariat gate, stopped and then hurled two small bombs that exploded with loud noises, creating panic among officials," he said.
The opposition Bangladesh Nationalist Party (BNP) has been leading angry protests since one of its leaders, Ilias Ali, went missing on April 17 in a case it believes was an abduction by the security forces.
Five small bombs exploded at the start of the latest strike on Sunday at Mirpur in northern Dhaka and two more exploded in front of the opposition headquarters in the city, police officers told AFP.
The BNP supporter who died on Saturday was hit by three bullets in the southern town of Lakshmipur during a fight between BNP and ruling Awami League party workers, police inspector Monirul Alam said.
"He died of his wounds after he was rushed to a hospital," Alam told AFP, adding another person was also critically injured.
Three BNP activists were killed last week in clashes with police in Ali's constituency in northeastern Sylhet district.
Police found Ali's car abandoned in an upmarket district of Dhaka. His driver is also missing.
The BNP fear Ali has been killed and accuse the elite Rapid Action Battalion security force of abducting him, an allegation both the force and the government have rejected.
Ali is the highest profile opposition politician to have "disappeared" since Prime Minister Sheikh Hasina took power in January 2009.
Human Rights Watch (HRW) on Friday urged the Bangladesh government to order an independent investigation into the recent disappearances of opposition and political activists.
Quoting two Dhaka-based rights groups -- Ain-O-Sailash Kendra and Odhikar -- HRW said the disappearance of least 22 people had been documented in 2012 alone and more than 50 people since 2010.
The families of Premier Hasina and Khaleda Zia, head of the BNP, have competed for power for decades in Bangladesh with the personal rivalry between the two women often triggering street clashes between their parties.