The Prime Minister batted away calls for a Leveson-style inquiry into the issues, insisting he wanted to reach the truth quickly.
The comments, in a statement to MPs, came after Barclays boss Bob Diamond admitted he was disappointed that the rate-rigging scandal happened on his watch.
However, he signalled that he would fight for his job, saying he wanted to "make sure that it cannot happen again".
Barclays chairman Marcus Agius resigned this morning and announced an internal review into the bank's "flawed" practices.
Mr Cameron said the Serious Fraud Office were looking at whether any criminal prosecutions could be brought.
He went on: "I want us to establish a full parliamentary committee of Inquiry involving both Houses chaired by the Chairman of the House of Commons Treasury Select Committee.
"This Inquiry will take evidence under oath have full access to papers, officials and Ministers - including Ministers and Special advisers from the last government and it will be given, by the government, all the resources it needs to do its job properly."
Mr Cameron added: "This is the right approach because it will be able to start immediately it will be accountable to this House and it will get to the truth quickly, so we can make sure this can never happen again.
Labour leader Ed Miliband told MPs vowed to continue pushing for a "full and open" independent inquiry.
"I'm not convinced by his way forward because I do not believe it measures up to the scale of what is required," he said.
Mr Miliband told the Commons the only way to rebuild trust in the banking system was with a full, independent inquiry.
"However able or distinguished, politicians investigating bankers will not command the consent of the British people," he said.
"People are understandably angry about the way their banks let them down and I don't believe the proposed way forward is the way we can build the consensus that is required for change."
The Labour leader said there had already been a number of reports by parliamentary committees into the banking crisis.
"I appreciate the Leveson inquiry has been uncomfortable for all sides but that's the way it should be," he added. "We will continue to argue for a full and open inquiry, independent of bankers and independent of politicians."