Mr. Zarghun, the Hezb-e-Islami spokesman, said the bomber was a woman in her early 20s.
Two other leaders of the Jamaat-e-Islami have been sentenced to death by the tribunal.
His family and friends blamed Jamaat-e-Islami, the country's largest Islamist party, for the killing.
The issue has united Islamist parties, which have often had political and ideological differences with Jamaat-e-Islami.
As the uprising has grown, it has attracted leaders associated with the Hezb-e-Islami party.
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Earlier this month the tribunal charged Ghulam Azam, the former leader of Jamaat-e-Islami, with war crimes.
Last week, a special tribunal sentenced a former member of Jamaat-e-Islami to death in absentia.
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Supporters of the country's largest Islamist party, Jamaat-e-Islami, say the trials are politically motivated.
BBC: Dhaka police and protesters clash over war crime trials
In Bangladesh the fortunes of the Islamist Jamaat-e-Islami party plummeted in last December's election.
The biggest Islamic party, Jamaat-e-Islami, loathes him for breaking his promise to shed his uniform.
Jamaat-e-Islami a key partner in a former Bangladeshi government says the charges are politically motivated.
Islami said the rotor blade snapped off, the copter spun to the ground and burst into flames.
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While the Taliban refuses to negotiate with Kabul, Hezb-e-Islami long has engaged in talks with Mr. Karzai's government.
Senior Jamaat-e-Islami leader Delwar Hossain Sayeedi was convicted of murder, abduction, rape and torture, and sentenced to death.
They are being used less as a path to justice than to crush an opposition Islamic party, Jamaat-e-Islami.
With the moderate Jamiat-i-Islami as its central party, the government has acceptable Islamic credentials -- a core requisite.
Mollah and five other leaders of the Jamaat-e-Islami party have been on trial before Dhaka's International Crimes Tribunal.
Among those detained were Syed Ali Geelani, head of the fundamentalist Jamaat-e-Islami, which favors Kashmir's accession to Pakistan.
Jamaat-i-Islami, a hard-line Islamist party, Saturday afternoon announced a boycott of the Karachi polls in protest against election irregularities.
The Islamist Jamaat-e-Islami party said it withdrew its candidates in Karachi and the southern city of Hyderabad in protest.
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Hezb-e-Islami, the Islamist insurgent group led by anti-U.S. warlord Gulbuddin Hekmatyar and loosely allied with the Taliban, claimed responsibility.
Hezb-e-Islami spokesman Haroon Zarghun said the group had carefully planned the convoy attack.
All the 10 people charged by the tribunal so far are from opposition parties, eight of them from Jamaat-e-Islami.
Haider's family and friends suspect Jamaat-e-Islami in the attack, but the Islamic party issued a statement Saturday denying involvement.
Considered more moderate than the Taliban, Hezb-e-Islami has been engaged in peace talks with President Hamid Karzai's administration for years.
The recent violence is mainly blamed on the opposition Jamaat-e-Islami party, whose leaders are facing war crimes at the tribunal.
The Jamaat-e-Islami wants the trial of its leaders for crimes allegedly committed during the 1971 independence war to be stopped.
BBC: Dhaka police and protesters clash over war crime trials
The ordeal proved embarrassing for Usman Sharif, a candidate for the hard-line religious Jamaat-e-Islami party, in the southern city of Karachi.
Khan, an ethnic Tajik, is a former deputy to Ahmad Shah Massoud, the leader of Jamiat-e-Islami, who was killed in 2001.
Jamaat-e-Islami was a key partner in the former government of Khaleda Zia, a longtime political rival of Prime Minister Sheikh Hasina.
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