Such is the bad blood and mistrust between Prime Minister Begum Khaleda Zia and opposition leader Sheikh Hasina that the two women have not talked to each other for 14 years.
And that is not likely to change despite a grenade attack last week on a political rally which Hasina had just finished addressing. Khaleda offered to meet her to express condolences for the deaths of 19 people at the meeting. Hasina turned her down.
Commentators said it was the latest in a series of bomb attacks in public places, and have said national security is becoming a major problem in one of the world's poorest nations.
They have said the prime minister and the leader of the opposition must put aside their differences and work together.
"The irony is that the apparently unbendable attitude of the two ladies has cost this impoverished country dearly, especially in terms of crisis management," said Sirajul Islam Chowdhury, a former professor at Dhaka University and a political commentator. For all their differences, the two women share much.
Hasina is the daughter of Sheikh Mujibur Rahman, the father of Bangladesh's 1971 independence. He was president when he was assassinated in 1975 by rogue military officers.
Khaleda's husband, General Ziaur Rahman, took power shortly thereafter, but he too was assassinated in 1981.
Khaleda and Hasina were both in opposition when military ruler Hossain Mohammad Ershad was in power from 1982 to 1990. The two co-operated in the movement to oust Ershad, and have taken turns in power since then, but have never been close.
They have remained foes ever since Khaleda's Bangladesh Nationalist Party (BNP) won a closely fought election in 1991.
Hasina and the Awami League were in power from 1996 to 2001, after which the BNP returned to power. Inevitably, a win by one has led to charges of vote-rigging by the other.
The reason for the enmity stems in part from their feud over who played a greater role in the country's independence - Hasina's father of Khaleda's husband.
After independence in 1971, Mujibur was named father of the nation in the country's 1972 constitution.
But after Khaleda assumed power in 1991 her party downplayed Mujibur's role and pushed the idea that Khaleda's husband, an army major in 1971 who revolted against the Pakistani army, was also an equally important player in the independence struggle, making Hasina and her party furious.
Khaleda's government amended the constitution earlier this year to delete the reference that Mujibur was the father of the nation.
After Saturday's grenade attacks, newspapers and neutral politicians called on the two women to put aside their differences and work together.