Iajuddin Ahmed, who heads an interim administration until next January's general elections, met 10 ministerial advisers over the past two days in an attempt to resolve the crisis, but no breakthrough had been made, officials said on Sunday.
Sheikh Hasina, leader of a the Awami League's 14-party alliance and a key contender for power in Bangladesh, said on Friday that she would give the caretaker government another week to prove its neutrality and commitment to free and fair elections.
She has threatened to launch an indefinite blockade of highways and other protests from November 12, to achieve her demands.
The Hasina-led alliance has been demanding the removal of M A Aziz, chief election commissioner and his deputies, accusing them of bias towards the Bangladesh Nationalist Party (BNP), which ruled the country until its mandate expired last month.
But BNP leaders met Iajuddin on Saturday and asked him not to tell Aziz and his team to step down.
"Instead of being influenced by what the Awamis say, the caretaker government should firmly stand by the election commissioners so they can complete their assigned job of holding a free and peaceful election," Abdul Mannan Bhuiyan, the BNP secretary-general, told reporters.
The intensifying standoff could lead the impoverished country of 140 million people to more violence similar to last week's trouble when 30 people were killed and hundreds injured, political analysts believe.
The BNP and Awami League have vowed to face each other "on the streets" - raising a security alarm.
"We are facing a potentially dangerous situation, which needs to be tackled immediately," a senior police officer said on Sunday.