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.
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.
BBC: Bangladesh strike over war crimes trials sparks clashes
In Bangladesh the fortunes of the Islamist Jamaat-e-Islami party plummeted in last December's election.
Islami said the rotor blade snapped off, the copter spun to the ground and burst into flames.
CNN: 2 killed as helicopter crashes into crane in central London
Senior Jamaat-e-Islami leader Delwar Hossain Sayeedi was convicted of murder, abduction, rape and torture, and sentenced to death.
Haider's family and friends suspect Jamaat-e-Islami in the attack, but the Islamic party issued a statement Saturday denying involvement.
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.
Liaqat Baloch, secretary general of Pakistan's most popular Islamic party, Jamaat-e-Islami, said members of his party were strongly considering boycotting the elections.
Eight of the 10 suspects indicted by the war-crimes tribunal are from Jamaat-e-Islami, an ally of the main opposition Bangladesh Nationalist Party.
Abdul Kader Mullah, 64, the assistant secretary general of the Jamaat-e-Islami, was found guilty of five out of six charges, including murder.
Observers now expect the verdicts in the cases of senior Jamaat-e-Islami leaders such as Mr Sayeedi and Mr Azam to follow rapidly.
While the Taliban refuse to negotiate with Kabul, Hezb-e-Islami has long been engaged in talks with the government of Afghan President Hamid Karzai.
They want Pakistan to be central to any peace deal Mr Karzai may strike with insurgent groups, including Hizb-e-Islami and the Haqqani network.
Ten others are on trial, including eight top leaders of Jamaat-e-Islami and two members of the opposition Bangladesh Nationalist Party (BNP), one a former minister.
Mr Sayadee is a leader of a prominent Islamic party, Jamaat-e-Islami.
Except for the Jamaat-e-Islami, parties have nothing to do with ideology.
In recent years, Ms. Hasina's government has effectively cracked down on the terrorist group Harakat-ul-Jihad-al-Islami, which used Bangladesh as a staging ground for attacks in India.
As some of the cases at the special tribunal into war crimes have reached their final stages, there are concerns that Jamaat-e-Islami may intensify its protest.
Sayeedi's Jamaat-e-Islami party says the tribunal is biased against it.
The BNP has maintained an electoral alliance with the Jamaat-e-Islami since 2001 and many in the party feel the alliance gives them their best chance of returning to power.
While most attacks in the Afghan war are carried out by the Taliban, the explosion on Thursday was claimed by Hezb-e-Islami, a smaller insurgent group led by warlord Gulbuddin Hekmatyar.
The Northern Alliance, and in particular the Tajik-dominated Jamiat-i-Islami faction, which controls Kabul, has little apparent reason to go along with a process that is likely to dilute its power.
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