The controversial article, published in The Washington Times, that sought US sanctions against Bangladesh sparked a political row in the country.
"Why don't you (Zia) sue The Washington Times if the signature is really fake?" the private UNB news agency quoted Prime Minister Hasina as telling a rally.
Hasina also questioned how the US newspaper could show "such an audacity by publishing the article in the name of Khaleda Zia if she did not write it at all".
The article was published on January 30 under a title 'ZIA: The thankless role in saving democracy in Bangladesh' but the controversy over the write-up began last week when the United States scrapped Bangladesh's preferential trading status over workers rights and safety issues.
Hasina alleged Zia and her party now disowned the article to "escape blames" for the US suspension of Generalised System of Preferences (GSP) for Bangladeshi products while senior BNP leaders earlier appreciated and justified the write up.