Sabir Husayn Chowdhury, political secretary to Awami League leader Shaikha Hasina Wajid, said many people were still being treated for injuries from Saturday's blasts.
The blasts occurred as the main opposition leader, Shaikha Hasina, was addressing the rally from atop a truck outside her party's headquarters in central Dhaka.
Visibly shaken, she crouched low in the truck soon after the first blast occurred at about 5am (1100 GMT), a witness said. But she was unhurt, her party said.
More than 300 people were injured, including senior opposition members, United News of Bangladesh reported.
Witnesses said many people were taken to hospitals. "People were covered with blood. Many injured were crying for help," said Muhammad Yasin, a rickshaw driver near the scene.
The toll could increase as some of the injured were in critical condition, doctors said, adding that one opposition member, Ivy Rahman, had lost both her legs.
Shaikha Hasina (R) may have
been the target of the attack
No one claimed responsibility for the blasts, but Awami League General Secretary Abd Al-Jalil said the target might have been Shaikha Hasina.
Prime Minister Khalda Zia condemned the "dastardly attack on a political rally", and said her government would try to find those responsible.
"Let us all work together to prevent repeat of such cowardly attacks," she said in a statement.
The rally had been called to protest against a series of bomb blasts early this month that killed two people, including an opposition supporter, in the northeastern city of Sylhet.
"It was so ghastly and so terrible that I've no words to describe," said Faruk Khan, an opposition lawmaker who was standing close to Shaikha Hasina.
Initial reports put the number of
wounded at more than 100
"It seemed to me that some of the bombs were thrown from multi-storey buildings near the scene," he said, estimating that at least 15,000 people were at the rally when the explosions occurred.
Doctors at Dhaka's state-run hospital appealed for blood and said they were overwhelmed with the number of injured people, many of whom arrived in slow-moving rickshaws.
Angry opposition supporters smashed and burned dozens of passing vehicles and shouted anti-government slogans to protest against the attack as police and paramilitary troops patrolling central Dhaka fired tear gas to disperse the crowd, witnesses said.
Violence spread to a dozen other cities and towns, where protesters smashed vehicles and attacked shops, witnesses said. Security was stepped up across the country, the authorities said.