At least four people have died in fresh clashes in Bangladesh, amid a row over who will run a caretaker government to oversee elections in January.
Bangladesh's transfer of power has sparked a major confrontation
Hundreds of people were injured as police fired teargas to disperse opposition demonstrators in Dhaka.
Government and opposition officials have been meeting President Iajuddin Ahmed to try to resolve the crisis.
They pledged to find a replacement for the man who had been named as interim head of government after he withdrew.
Presidential spokesman Rahman Chowdhury said the nominated interim PM, ex-Chief Justice KM Hasan, had declined the post.
The opposition Awami League had already made clear it would not accept Mr Hasan - whom it described as a supporter of the governing Bangladesh National Party and a stooge of the government.
Outgoing PM Khaleda Zia, whose mandate expired at midnight, could stay in office as a caretaker for up to 15 days if the two sides fail to reach agreement on a new interim leader.
The opposition Awami League and its allies had threatened to paralyse the country if Mr Hasan took office. Police responded by using with teargas and rubber bullets to disperse their demonstrations.
Saturday's unrest included explosions and gunfire in the capital Dhaka. The latest deaths bring to at least nine the number of people killed since Friday.
Khaleda Zia said the transfer of power will go ahead
Roads have been blocked and outbreaks of violence have been reported in other parts of the country.
Under Bangladesh's unique system, when an administration comes to the end of its term, it hands over to an unelected interim government which has 90 days to organise elections.
The opposition has been demanding a say in choosing the "chief adviser", as the interim prime minister is known.
Mrs Zia appealed for calm as the fresh wave of violence hit the country.
She promised the poll would be free and fair, and said the constitution would "safeguard a peace-loving and responsible nation".
Not on speaking terms
The BBC's Roland Buerk in Dhaka says Bangladeshi politics is especially bitter because of the personal rivalry between Sheikh Hasina of the Awami League and Mrs Zia.
They have led the country in alternate terms since 1991 but have not spoken for years.
Parliament has been boycotted regularly by whichever party is in opposition, and a culture of street demonstrations has developed.
The BNP is calling for its supporters to be ready to take on opposition activists.
Our correspondent says that there will be little the 25,000 police and security personnel deployed in the capital, Dhaka, can do as the powerful political parties try to enforce their dominance of the streets.
With the elections not expected to take place until January, months of disruption could lie ahead, our correspondent adds.