"The metropolitan magistrate court asked police to investigate into the allegation under section 123 (A) of the Penal Code after obtaining required government clearance," a court official told PTI.
He said the order came after a brief hearing on the charges against the 70-year-old ex-prime minister brought by a lawyer for her "slanderous comments" about the martyrs of the liberation war in which three million people were killed.
Legal experts said the government clearance was a pre-requisite for investigating or trying anyone under the section which is generally known as "sedition charge".
The development came as another lawyer last week served Zia a legal notice asking her to apologise to the nation within seven days or face legal consequences.
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Speaking at a discussion on December 21, Zia "expressed doubts" about the casualty figures of 1971 and commented that Bangladesh's founder Bangabandhu Sheikh Mujibur Rahman actually wanted to be undivided Pakistan's Prime Minister rather than lead the country to independence.
Zia's BNP is a crucial ally of fundamentalist Jamaat-e- Islami, which was opposed to Bangladesh's independence from Pakistan.
The ruling Awami League, 1971 veterans and members of the martyred families sharply reacted to her comments with some of them even calling her as the "agent of Pakistan".
"The stance of Pakistan, the Jamaat-e-Islami and the BNP is the same regarding the 1971 genocide and the ongoing war crimes trial... She (Zia) simply reconfirmed her stance," said Shahriar Kabir, who heads a forum that have been campaigning for the punishment of the major Bengali-speaking perpetrators of 1971 atrocities who sided with Pakistani troops during the war.