Barclays was "not alone" in efforts to rig a key interest rate benchmark, George Osborne told MPs as he said the scandal exposed a systemic failure in the financial system.
The bank was fined £290 million by US and UK regulators for trying to manipulate the rates at which banks lend to each other to boost its profits.
Updating MPs on the case, Mr Osborne said the bank's chief executive Bob Diamond had "very serious questions to answer" about what he knew and when.
The fine was imposed on Barclays by the Financial Services Authority (FSA) and US regulators over attempts to rig the Libor (London Interbank Offered Rate) and Euribor interbank lending rates.
But Mr Osborne told MPs: "Barclays are not alone in this. The FSA is continuing to investigate the conduct of a number of other banks in relation to Libor."
Mr Osborne said the Government would also consider the possibility of applying criminal sanctions to directors of failed banks "where there is proven criminal negligence".
Fines paid to the FSA are used to reduce the levy paid by other institutions, but Mr Osborne said he was considering changes to ensure that penalties "of this nature go to help the taxpaying public not the financial industry".
Officials would examine whether the move could be backdated to cover the fine imposed on Barclays.
Mr Osborne said: "It is clear that what happened in Barclays, and potentially other banks, was completely unacceptable, was symptomatic of a financial system that elevated greed above all other concerns and brought our economy to its knees."
"A number of individuals" are under investigation by the FSA and "this number is expected to increase".
The Serious Fraud Office is aware of the matter and is in talks with the FSA, he added.
Turning to Mr Diamond, the Chancellor said: "As far as the chief executive of Barclays is concerned, he has some very serious questions to answer today.
"What did he know and when did he know it? Who in the Barclays management was involved and who, therefore, should pay the price?"
The Treasury Select Committee has asked him to appear and Mr Osborne said: "We all want to hear his answers."
He added: "The story of irresponsibility is not over yet. Our financial services should be a source of economic strength and national pride for this country.
"But failures in our banks and financial system have cost the country billions and put thousands out of work.
"Those responsible should be held responsible."
Mr Osborne said shadow chancellor Ed Balls, who was a Treasury minister when Barclays' traders were manipulating Libor and who was not in the Commons for today's statement, should "account for himself".
The Chancellor told MPs: "He was there every single day while these abuses were taking place as the City Minister responsible for regulating Barclays and other banks at the time."
Shadow chief secretary to the Treasury Rachel Reeves condemned the culture which, she said, allowed the "price-fixing scandal" to unfold.
She added: "People thought they could do anything they liked just to make a fast buck.
"They thought they would never be held to account, thinking they were effectively above the law."
She believed the scandal illustrated Labour leader Ed Miliband's fears over "predatory capitalism".
Ms Reeves said: "This is one of the worst cases yet. The public have been assured that the banks have cleaned up their act, ordinary borrowers and savers were told they could trust the banks again.
"But these unfolding revelations shine a new light on shocking practices in one of Britain's most important banks.
"What should have been an impartial exercise in reporting independent interest rate statistics became an exercise in cooking the books, cheating the system and fixing the market."
She called on the Government to consider involving the Serious Fraud Office, Office of Fair Trading and City of London Police, and demanded to know if an investigation would be launched into the bank's auditors.
Ms Reeves said people deserved to learn who knew what and when, adding: "Criminal prosecutions should and must follow against any of those who may have broken the law."
She urged ministers to regulate Libor through an amendment to the Financial Services Bill which is going through Parliament.
But Mr Osborne claimed the Bill would address systematic abuses, saying: "The Government has been reviewing Libor, awaiting publication of this report which we knew was coming.
"We have considered it carefully and we are looking at criminal sanctions for market manipulation."
Conservative chairman of the Commons Treasury select committee Andrew Tyrie asked what was now left of trust between Parliament and the banks.
He said Barclays and "probably other banks" were "rigging the markets at a crucial time in the last crisis", adding that the Treasury committee would now investigate this properly.
Mr Tyrie asked the Chancellor to amend the Financial Services Bill to include both derivatives and Libor in the legislation before Parliament.
Mr Osborne said the Government was looking at strengthening the criminal sanctions regime in general for market abuse and manipulation.
Former Labour chancellor Alistair Darling said: "We're kidding ourselves if we think that this was the only country where this sort of thing was going on.
"The American authorities are just as concerned as our authorities, and it is symptomatic of a culture that prevailed for a lot of the last decade, where frankly anything was allowed to go."
He suggested Libor had to have some degree of independent supervision and "can't be a work of fiction".
He urged the FSA to "take out of banks and put off the road those people who were responsible for doing this, those people who've tolerated it and those people who gained and condoned it".
He added: "If that isn't done, then we have no chance whatsoever of moving on from this in what remains a very important industry for this country."
Mr Osborne said the FSA was pursing cases against individuals.