Gordon Brown's competence as PM has come under fire during heated Commons exchanges following the donations row.
Mr Brown has said the donations were unlawful
David Cameron said there had been "disaster after disaster" since Mr Brown took over, and asked if he was "cut out for the job".
Lib Dem acting leader Vincent Cable said Mr Brown had gone "from Stalin to Mr Bean" in a matter of weeks.
Mr Brown said he would be judged on his record for delivering low inflation and investing in the NHS and education.
It has emerged that property developer David Abrahams has given Labour more than £650,000 under other people's names over four years - something Mr Brown has described as unlawful and "completely unacceptable".
Labour's treasurer Jack Dromey repeated the phrase "complete concealment" when he was asked by reporters if he knew about the arrangement, or whether he was kept in the dark.
The party's general secretary Peter Watt has already resigned after admitting he knew about it and Mr Brown has announced an inquiry.
Labour's chief fundraiser Jon Mendelsohn said he was told about it last month and was unhappy about it and determined it would not continue, but did not tell anyone else as he wanted to sort out the matter with Mr Abrahams personally.
Mr Brown has said he had "no knowledge" of the nature of the donations - but during heated exchanges at prime minister's questions, Mr Cameron said his explanation "beggars belief" and "goes to questions of the prime minister's own integrity".
"We have had 155 days of this government. We've had disaster after disaster. A run on a bank, half the country's details lost in the post and now this.
"His excuses go from incompetence to complacency and there are questions about his integrity. Aren't people rightly asking now, is this man simply not cut out for the job?"
In response Mr Brown pointed to Mr Cameron's role in "Black Wednesday" in 1992 - when the UK crashed out of the European Exchange Rate Mechanism.
He said competence was delivering low inflation, low interest rates, the highest employment for a generation and more investment for the NHS and education.
He said he had acted immediately to set up two inquiries into Mr Abrahams' donations and said: "All of us on all sides of this House have an interest in integrity in funding to political parties."
Asked why he had not "called in the police" if he thought something unlawful had taken place - Mr Brown said Labour had followed convention in reporting it to the Electoral Commission.
Letter to police
He added: "We are happy to cooperate in any way because in my view this is something that has got to be cleaned up in the interests of the whole of public life and I'm determined to take that action."
Acting Lib Dem leader Mr Cable made reference to a comment by the former civil service boss Lord Turnbull, who said Mr Brown as chancellor had operated with "Stalinist ruthlessness".
Mr Cable said: "The house has noticed the prime minister's remarkable transformation in the last few weeks from Stalin to Mr Bean, creating chaos out of order rather than order out of chaos."
Mr Abrahams said he used intermediaries to avoid publicity
Speaker Michael Martin had to repeatedly warn MPs to stop shouting as a succession of senior Tory MPs taunted Mr Brown.
Michael Ancram suggested Mr Brown's officials liked to keep him "in the dark", while another Tory MP, Peter Tapsell asked whether finally becoming prime minister had turned into a "poisoned chalice".
Meanwhile the Liberal Democrats have referred the matter to the police. Acting leader Vincent Cable has urged them to investigate apparent "serious breaches" of party funding laws.
In the Commons Mr Brown defended Mr Mendelsohn, saying he had only started in the job from 3 September, while the donations stretched back over four years, and had "absolutely no involvement" in the donations.
And he said there was not "one iota" of evidence that his deputy leader, Harriet Harman, who has admitted accepting money in Janet Kidd's name - which later turned out to be from Mr Abrahams - knew about its true origins before Saturday.
Meanwhile Janet Dunn, the fourth person to be named as one of Mr Abrahams' intermediaries, who said on Tuesday she knew nothing about the £25,000 donation in her name, has since said that was inaccurate.
She said the whole issue had come as a "complete surprise" and she had not intended to mislead - after reviewing her records she found a cheque to the Labour Party was drawn on her account in 2003.