Mr Brown says talks on bonuses will be part of the package
Prime Minister Gordon Brown says he is "angry" about irresponsible behaviour by bankers and has warned that "the days of big bonuses are over".
The problems began in the US but there had been "abuses" in the UK, he said.
Meanwhile Employment Minister Tony McNulty has told the BBC Britain "may well" be heading for a recession.
Lib Dem leader Nick Clegg has said bank executives whose actions contributed to the crisis should be removed.
On Wednesday the government announced a £400bn rescue package for the banking system, a day after share prices in UK banks plunged.
Mr Brown is visiting Birmingham on Thursday, part of a tour of the country to "explain" the banking rescue to voters.
The prime minister's spokesman said he would be meeting small businesses and would head to the south west on Friday while regional ministers would also play a role in explaining why action had to be taken.
In the GMTV interview earlier, Mr Brown was asked what he would tell taxpayers who were angry that public money was being used to prop up failed banks.
"I'm angry too. I am angry at irresponsible behaviour," Mr Brown said.
"Our economy is built around people who work hard, who show effort, who take responsible decisions, and whether there is excessive and irresponsible risk-taking, that has got to be punished."
He said it was important for everyone to have a banking system they could trust and it was "completely unacceptable" to take excessive risks.
"The days of big bonuses are over. One of the conditions of us helping the banks is that we will have to reach an agreement about their executive remuneration," he added.
He said the package announced on Wednesday was a "restructuring" of British banks to ensure they provided security and said other countries around the world were "looking at what we are doing".
"Most of this has come out of America and then affected the British banking system, but there have been abuses in our system as well and these have got to be dealt with too," he said.
"Where these guys have taken irresponsible risks, that is completely unacceptable."
Meanwhile Tony McNulty, minister of state for employment and welfare reform, told BBC 2's the Daily Politics the success of the rescue package would be a "precursor to how deep and how long the recession will be".
He added: "We're slowly getting to a stage where the slowdown may well turn technically into recession and then we'll be talking about the nature and depth of the recession."
Asked whether he agreed with those comments later, the prime minister's spokesman said the Treasury would update its economic forecasts in the autumn pre-Budget report.
The government has offered eight leading banks up to £25bn capital in return for preference shares.
It says action on bonuses and dividends will take two forms - the Financial Services Authority is looking at how it can ensure responsible risk taking while the issue will be part of conditions attached to banks accepting public money.
Later Liberal Democrat leader Nick Clegg wrote to Mr Brown to urge him to take steps to remove senior executives whose actions had contributed to the economic crisis to ensure they were not "let off the hook".
He also said board members on banks should not get bonuses, to stop them following "distorted business models".
"The government's rescue package must be used as a starting point to reform the way banks operate to ensure this crisis is never repeated," he said.
On Wednesday, Conservative leader David Cameron said taxpayers would be "infuriated" if the public money went on bonuses for failed executives.
Earlier the Conservatives called for emergency pension protection while the economic turmoil continues, saying those who are about to take out a pension annuity at a fixed rate need to know their money is safe.
Shadow work and pensions secretary Chris Grayling said: "If you happen to reach the point at which that happens - your retirement date, or your 75th birthday - this week, at a time when the markets are very turbulent, they're very up and down, it puts huge pressure on you."
Initially £25bn of taxpayers' money will be used to kick-start lending between eight banks and building societies - in return for preference shares in them. A further £25bn will be available if necessary for other institutions.
The government has also offered a further £250bn in loan guarantees, and increased another lending scheme to £200bn.