Awema's chief executive Naz Malik and finance director Saquib Zia were sacked in February.
She would then be replaced by her nemesis, Khaleda Zia, of the opposition Bangladesh Nationalist Party.
Jamaat is an ally of the BNP, which is led by former Prime Minister Khaleda Zia.
Ms Zia says the war crimes trials are politically motivated to target the opposition.
The trial against Khaleda Zia, prime minister till October 2006, is yet to begin.
But so were similar plans by General Ayub Khan in 1960 and General Zia in 1984.
The League has 229 of 300 parliamentary seats compared with 31 for Mrs Zia's BNP.
Zia ul-Haq enlisted the help of former World Bank and IMF officials in his cabinet.
Pranab Mukherjee, India's finance minister, called on Mrs Zia recently, inviting her back to Delhi.
ECONOMIST: The prime minister sets the country on a dangerous path
But India's habit of shunning meetings with Mrs Zia and her followers may come to look short-sighted.
This technique, Dr Zia said, had been adopted elsewhere to operate on lower parts of human body.
Zia ul Haq, his successor, tried to legitimise his military coup by pledging to Islamise the country.
"If we think that Shoaib Akhtar's bowling action is alright, we can play him in Tests, " said Zia.
Zia took power in 1977, in a coup that displaced Zulfikar Ali Bhutto, the father of Benazir Bhutto.
Lunching with Zia Audin was a ritualistic courtesy, demanded by custom and protocol.
Two weeks later Zia Audin quietly abandoned Castle Greyskull and fled to Kabul.
Pakistan's army, nine years after the death of General Zia ul-Haq, the last military dictator, is in cautious mood.
Mrs Zia alleges that the Election Commission favours the League and should resign.
When Zia Yusuf, now president and chief executive of San Francisco-based Streetline Inc.
Mrs Zia chuckles that she will go after Delhi's summer heat is past.
ECONOMIST: The prime minister sets the country on a dangerous path
The administration Mrs Zia headed from 2001 to 2006 was a brutal kleptocracy.
Zia ul-Haq, could count on uncritical support from the West because Pakistan was a vital cog in the Cold War.
She's head of the Bangladesh Nationalist Party and widow of the former president, Zia Rahman, who was assassinated 25 years ago.
On Monday, Prime Minister Zia visited some of the injured in a Dhaka hospital, including senior Awami League leader, Ivy Rahman.
BBC: Protesters in Dhaka demand the resignation of the premier
All of the American and Afghan agencies around the region knew this, and most interestingly Zia Audin knew that we knew.
They were from General Lodin's command and Zia Audin theoretically reported to them, although they exercised no real control over him.
"If they are not going to fulfil their obligation, we are not going to tour New Zealand, " said chairman Tauqir Zia.
Zia has called the tribunal a farce, while Hasina has urged Zia to stop backing those she says fought against independence.
Jamaat-e-Islami was a key partner in the former government of Khaleda Zia, a longtime political rival of Prime Minister Sheikh Hasina.
Two years later, after Zia ul-Haq was killed when his plane dropped out of the sky, she was elected to power.
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