On Friday, Sheikh Hasina said the government had already met many of the group's demands.
Mrs Zia's family dynasty, also corrupt, is as against India as Sheikh Hasina's is for it.
But the Awami League, led by the prime minister, Sheikh Hasina, is taking no chances.
This week the first of four cases filed against Sheikh Hasina appeared close to collapse.
Prime Minister Sheikh Hasina has made prosecuting war crimes a key goal of her government.
BBC: Huge Bangladesh rally seeks death penalty for war crimes
Sheikh Hasina has used this mandate to consolidate power and hound her enemies, real and imagined.
As Sheikh Hasina looks ever more strident, people may start tiptoeing away from her.
ECONOMIST: The prime minister sets the country on a dangerous path
Sheikh Hasina is the daughter of Sheikh Mujibur Rahman, Bangladesh's independence hero, murdered in 1975.
Sheikh Hasina will not, says a senior politician, want to pull the tiger's tail.
Sheikh Hasina's control of the League remains absolute, and she appears confident of victory.
He is said to be in hiding, but Sheikh Hasina has promised that he will be punished.
BBC: Dhaka building collapse: Fears for hundreds still missing
More preoccupying to the prime minister, Sheikh Hasina, are the implications for her attempted rapprochement with India.
ECONOMIST: India��s shoot-to-kill policy claims one more innocent
The Bangladeshi Taka has been de-valued eleven times since the government of Sheikh Hasina was elected last year.
Prime Minister Sheikh Hasina called for special prayers for the victims to be held across the country on Friday.
For India, however, the risk is that it is betting too heavily on Sheikh Hasina, who is becoming increasingly autocratic.
He says he has done nothing wrong and will only resign if the prime minister, Sheikh Hasina, tells him to.
ECONOMIST: A foreign-funded bridge is hostage to murky local politics
Bangladeshi Prime Minister Sheikh Hasina "expressed gratitude to the Almighty" and encouraged people to "offer thanksgiving prayers", her spokesman told reporters.
"It's a miraculous event, " Prime Minister Sheikh Hasina said after visiting Ms. Begum in the hospital and congratulating the rescue teams.
Jamaat-e-Islami was a key partner in the former government of Khaleda Zia, a longtime political rival of Prime Minister Sheikh Hasina.
Like Sri Lanka's president, Mahinda Rajapaksa, did last year, Sheikh Hasina has used the forms of parliamentary democracy to undermine the substance.
Prime Minister Sheikh Hasina visited Ms. Begum in hospital on Friday evening.
Meanwhile, the army appears to have resigned itself to Sheikh Hasina's becoming the next prime minister or, at least, contesting the elections.
Jamaat is an ally of the BNP, Sheikh Hasina's bitter political rivals.
BBC: Huge Bangladesh rally seeks death penalty for war crimes
General elections are due in Bangladesh in July and Sheikh Hasina is being challenged by opposition leader and former prime minister, Khaleda Zia.
Prime Minister Sheikh Hasina visited the site and some of the victims in hospital, assuring them they would receive help from the government.
BBC: Dhaka factory collapse: Owner Rana faces anger at court
For example, Aung San Suu Kyi, Megawati Sukarnoputri and Sheikh Hasina each wrote about their fathers, Aung San, Sukarno and Mujibur Rahman respectively.
This week walls near the Dhaka offices of Sheikh Hasina were plastered with posters of Felani that called for the killing to stop.
ECONOMIST: India��s shoot-to-kill policy claims one more innocent
"Those who're involved, especially the owner who forced the workers to work there, will be punished, " Prime Minister Sheikh Hasina told lawmakers on Friday.
Bangladeshi PM Sheikh Hasina has firmly rejected demands by Islamists for a new anti-blasphemy law to punish those who defame Islam and Prophet Muhammad.
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