Seven small bombs exploded in the Bangladeshi capital Dhaka on Sunday, police said, after an opposition supporter was shot dead in clashes ahead of a fourth nationwide strike in eight days.

Security was tight across the country with around 10,000 policemen deployed in Dhaka after the bombs exploded in the morning as 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.

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.

The BNP supporter 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 other 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 Bangladesh 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 was documented in 2012 alone and more than 50 people since 2010.