They say he has drawn up a list of voters for forthcoming elections that includes 10 million fake names.
A caretaker government is currently in place to oversee January's poll.
"We told the president that he had failed to prove that he is neutral," said Obaidul Kader, a senior Awami League leader.
"We had set Sunday evening as the deadline to remove the chief election commissioner and his deputies. But he failed. The deadline has passed and we will now resume our nationwide blockade Monday morning."
Mahbubul Alam, a member of the interim government said on Saturday that the government had come up with a package of measures it believed would end the impasse.
The president was expected to reveal the proposals in a televised address to the country over the next few days.
Last week's four-day blockade shut everything from schools to ports and many people left Dhaka ahead of the latest stoppage fearing violence or being stuck in the city.
Police have ordered an indefinite ban on the carrying of weapons and sticks during rallies or demonstrations in Dhaka and other main cities from Monday.
Two people were killed during clashes between the parties during the four-day protest.