Dhaka, Oct 27 (IANS): Bangladesh Prime Minister Sheikh Hasina and her rival Khaleda Zia Saturday discussed the possibility of a dialogue between ruling and opposition parties to end the stalemate over a caretaker government to oversee elections, Xinhua reported.

The two leaders talked to each other over phone for 37 minutes. It was the first direct conversation between them since 2009.

Prime Minister Hasina invited Khaleda Zia, the Bangladesh Nationalist Party (BNP) chairperson, to Gono Bhaban, the former's official residence, Monday evening to discuss about the caretaker government, said a BNP official requesting anonymity.

Hasina, also the ruling Bangladesh Awami League (AL) party president, urged the BNP chief to withdraw her call for a three-day strike from Sunday morning, the official added.

BNP chief accepted Hasina's invitation for holding dialogue, but deferred the premier's proposed date.

"We'll hold talks but cannot withdraw the hartal (shutdown)," Khaleda's press secretary Maruf Kamal quoted her as saying to Hasina during the 37-minute phone conversation.

Zia also said the dialogue could be held after the shutdown.

On Friday, Bangladesh's main opposition called a three-day nationwide shutdown from Sunday morning to press its demand for restoration of the non-party caretaker government system to oversee the national elections slated for early 2014.

Zia announced the shutdown at a grand rally in capital Dhaka, giving Hasina government two-day ultimatum for initiating a dialogue on a neutral election-time government.

At least six protesters were killed and about 500 injured when anti-government protesters and activists of the ruling party fought pitched battles Friday in different parts of Bangladesh.