Rallies were also reported in other cities across the country.
It came a day after some 20,000 demonstrators spontaneously took to the streets of the capital, angry over the deaths of 32 people in Friday`s fire.
Concerns that safety was compromised because of corruption - a long-standing issue in Romania - have fuelled public anger against the political elite, including Mr Ponta.
`Country is rising up`
Mr Ponta, who is currently facing trial on corruption charges, said in a televised address that he hoped his government`s resignation would "satisfy the people who came out in the streets".
The mayor of the district of Bucharest where the nightclub fire occurred and the country`s Interior Minister Gabriel Oprea also stepped down on Wednesday.
For a second consecutive night, protesters gathered late on Wednesday in University Square, a hub for anti-government rallies in central Bucharest.
They marched toward parliament with protesters urging others to join in as they went, shouting: "Get out of your homes if you care`` and "Don`t be afraid, the country is rising up."
Demonstrators have been complaining of government corruption and poor safety supervision, and say they see Mr Ponta`s resignation as just the beginning of reform for the political elite.
The cities of Cluj, Timisoara and Constanta saw similar rallies on Wednesday.
President Klaus Iohannis, who has repeatedly called on Mr Ponta to step down since the corruption scandal unfolded in June, called for a "sea change" in Romanian politics in the wake of the resignations.
He also voiced praise for Tuesday`s protests, saying the club tragedy had "affected the nerve of the nation".
Mr Ponta, who in September became the first sitting Romanian prime minister to go on trial for corruption, denies the charges.
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