The 14-party alliance, led by Sheikh Hasina's Awami League, resumed an indefinite nationwide strike on Monday after the interim government failed to meet a Sunday deadline to remove Aziz and his three deputies over allegations of bias.
The alliance accused Aziz of bias in favour of the former prime minister Begum Khaleda Zia.
Thousands of protesters filled the streets and highways of Dhaka on Wednesday, cutting off the capital's links with the rest of the country.
On Tuesday, armed partisans of Zia attacked a procession of former supporters who broke away to form a new party in southeastern Chittagong city, said Mohammad Ali, a spokesman for the breakaway faction.
Two supporters of the breakaway Liberal Democratic Party were badly beaten and died later in a hospital in Chittagong, said Ajoy Deb, a doctor.
A statement issued by Zia's party denied responsibility for the attack.
The Liberal Democratic Party is not part of the 14-party alliance led by Sheikh Hasina but it supports the strikes.
Zia's coalition held power until October before handing over power to an interim government, headed by the Bangladesh president.
The interim government will oversee elections in January. Hasina, a former prime minister, was the main opposition leader during Zia's five-year tenure.