Friday night's blaze in Bucharest started when a band performing at the club set off fireworks.
Demonstrators called for Ponta to step down, complaining of government corruption and poor safety supervision.
Ponta said on Wednesday that he and his government were standing down.
"I hope the government's resignation will satisfy the people who came out in the streets," he said on Romanian TV, the report reads.
"Victor Ponta is giving up his mandate. Someone needs to assume responsibility for what has happened. This is serious matter and we promise a quick resolution of the situation," the head of the ruling leftist Social Democrat Party Liviu Dragnea told reporters in parliament.
More than 100 people are still in hospital and some of them in a critical condition, after suffering burns and poisoning in the 30 October fire. Doctors fear the toll could rise.
