The Opposition has filed a motion of no confidence in the government following the prime minister's failure to dismiss minister Konrad Mizzi and his chief of staff Keith Schembri.
In a reaction, the government said it would propose that the motion be debated in parliament next week.
Addressing a press conference in Parliament, Opposition leader Simon Busuttil said the Panama scandal had been rumbling for seven weeks, but Dr Muscat had not done anything about it.
Dr Mizzi, he pointed out, is the only minister in the EU who has been named in the Panama Papers scandal.
His trust in New Zealand and company in Panama were revealed by journalist Daphne Caruana Galizia seven weeks ago and the Panama Papers showed that he had also attempted to set up bank accounts in Dubai and Panama.
The Opposition leader said that the situation was no longer tenable and could not be sustained any longer. The Prime Minister should now shoulder responsibility for his actions and resign.
Asked whether he heard the persistent rumors that Dr Muscat was about to sack Dr Mizzi and Mr Schembri, Dr Busuttil said the Prime Minister was seven weeks late.
"The suspicion is that Dr Muscat cannot act as he is also involved in this scandal," he said.