Bangladesh Prime Minister Sheikh Hasina and her arch rival Khaleda Zia held phone talks on Saturday, the first direct conversation between the two leaders of the South Asian country's politics since January, 2009 when her cabinet took oath of office.

They held talks to pave the way for dialogue between the ruling and the main opposition parties to end impasse over polls-time government formation.

Hasina invited the Bangladesh Nationalist Party (BNP) Chairperson Khaleda Zia, also two-time former prime minister, to Gono Bhaban, her official residence, Monday evening to discuss about polls-time government, said an official who preferred to be unnamed.

The official in BNP chairperson's office told Xinhua that Hasina, also the ruling Bangladesh Awami League (AL) party president, urged BNP chief to withdraw her call for a three-day non-stop strike from Sunday morning.

Footage from local Independent Television showed Hasina talked to Khaleda over mobile phone while saying repeatedly, "withdraw hartal, withdraw hartal."

"Please Join me in a dinner on October 28. You please come with the numbers of leaders you like."

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," Khleda's Press Secretary Maruf Kamal quoted her as saying to Hasina during the 37-minute phone conversation.

Khaleda Zia also said the dialogue can be held after the hartal.

Six protesters were claimed to be dead while 500 others were injured when Bangladesh's anti-government protesters and their ruling party rivals fought pitched battles for hours across the South Asian country Friday.

Khaleda Zia's BNP-led 18-party had earlier said October 25 is the last day of Hasina's government and asked its leaders and activists to take to the streets on the very day to press home its demand for the restoration of the non-party caretaker government system.

Khaleda on Friday called a three-day nationwide dawn-to-dusk non-stop shutdown from 6 am local time on October 27 to 6 pm on October 29.

She announced the strike at a grand rally in capital Dhaka, slapping a two-day ultimatum of Hasina's government for initiating dialogue on a neutral election-time government.

Incidents of clash, arson, vandalism, chase and counter-chase have been reported in many Bangladesh districts Saturday. A leader of Chhatra Shibir (the student wing of BNP's key ally Bangladesh Jamaat-e-Islami party) was reportedly killed and nearly a dozen people including many cops were injured as BNP and Jamaat men clashed with police in Rajshahi, some 256 km west of capital Dhaka, on Saturday afternoon.

In an apparent move to de-escalate tension between the ruling and opposition parties, Prime Minister Hasina on Oct. 18 proposed an all-party government be set up to hold general elections in the country.

But the BNP has rejected Hasina's all-party interim government proposal and tabled a new formula for the administration.

Since June 2011 when Bangladesh parliament abolished the non- party caretaker government system after an apex court verdict declared the 15-year-old constitutional provision illegal, the BNP- led alliance has been waging mass protests demanding for the reinstatement of the provision.

The scrapped provision mandated an elected government to transfer power to an unelected non-partisan caretaker administration to oversee a new parliamentary election on the completion of its term.

Khaleda has asked Hasina's AL to bring back the caretaker system, or else it won't participate in the next polls because it fears an election without the caretaker government will not be free and fair.

The parliament is due to expire on January 24 next year and elections should be held within 90 days before its expiry.

Khaleda warned on Friday that Hasina's government will be responsible for the consequences of what happens next if they don' t start dialogue to reach consensus about the polls-time government.

"Your government will be illegal from October 27," she said.

But AL presidium member Mohammad Nasim claimed that Hasina's ruling government would remain in office till January 24 as per the constitution.