They have not been on speaking terms for more than a decade. But now the "unthinkable" in Bangladesh's fractious politics may happen - former prime minister Khaleda Zia has agreed to sit and talk with arch rival Sheikh Hasina "in national interest".
The ball is now in the court of Hasina, also a former prime minister who is abroad for medical treatment and expected to return later this month.
Hasina's Awami League has cautiously reacted to this by laying a precondition that Hasina, now on parole and facing several corruption cases, be "released permanently" before such a meeting takes place.
Zia's Bangladesh Nationalist Party (BNP) too made an identical demand that the government release Zia and her sons to facilitate the dialogue.
Political observers said the caretaker government's efforts and the fast-moving political scenario may compel the two battling begums, who have dominated the political scenario for nearly three decades, to meet.
But they noted that besides their ego clash, the differences between the two are deep-rooted and political in nature.
The two represent rival political legacies that emanated from the freedom movement in 1971. Hasina is the daughter of the country's founding father Sheikh Mujibur Rahman and Zia the widow of Ziaur Rahman, who played a key role in the movement and later became the president.
Zia and Hasina had cooperated only once in 1990, to oust military ruler H.M. Ershad. They fell out thereafter.
The heads of BNP and AL have not met and spoken to each other for more than a decade. "Many consider the bitter relations between the two as the main obstacle to political stability in the country," said The Daily Star.
The military-backed government of Chief Adviser Fakhruddin Ahmed has been ready to broker the talks as part of preparations for the parliamentary polls it has committed for this December.
Commerce and Education Adviser Hossain Zillur Rahman, a key official who has been making the efforts, told media late on Friday that Zia, released on bail after over a year in jail, had agreed to sit with Hasina "to promote fair competition in politics and do away with mudslinging", The Daily Star said Saturday.
Zia, who heads the BNP and a four-party alliance, gave her word at a meeting with Rahman and three other advisers (ministers).
She also agreed to "help rid politics of bad elements" and draw up a code of conduct to ensure post-election stability.
During the over two-hour meeting, Chief Adviser Fakhruddin Ahmed called Khaleda and briefed her about the overall goals of his government. The conversation lasted 10 minutes, media reports said on Saturday.
Zia asked Fakhruddin to withdraw the state of emergency, imposed in January last year, without delay and hold the ninth parliamentary election before the upazila (sub-district) polls.
The government, that organised the civic elections in August, has been keen to extend the exercise at the sub-district level, but the political parties are insisting that the parliamentary polls be held first.
However, Zia, joining in with the government plans, agreed to work in unison towards a peaceful and credible national election by December.
"We've formally invited her (Khaleda) to dialogue with the government. She has consented to sit as soon as possible," Hossain Zillur Rahman said.
All major political parties except BNP and its ally Jamaat-e-Islami have had discussions with the government on electoral and other issues.
The government has a tough task ahead in dealing with the two women leaders and many of their ministers and lawmakers against whom corruption cases are pending in the courts.
Such cases have in the past been termed 'political' in nature and withdrawn to facilitate a political reconciliation.