Campaigners say more post offices will close unless action is taken
The Post Office must become a "people's bank", securing its future and helping more people set up accounts, MPs, unions and interest groups have said.
They outlined plans for a Post Bank, offering a wider range of financial services, backed by the government rather than a private institution.
Unions say this would help poor people and pensioners, while business groups say it could create up to 11,000 jobs.
Business minister Pat McFadden said there was "potential" in the idea.
However, there were several "different models" to look at, he added.
The Post Office has offered mortgages since 2003 and also provides savings accounts, insurance, personal loans and credit cards.
The Post Bank Coalition's proposals include branches offering tailored products to small businesses and a "universal banking obligation" - to ensure all people have access to accounts.
There are also calls for links with credit unions, to ensure post offices have closer ties to the local economy.
Post Bank should be set up with government funding and not be run by the Bank of Ireland, as is currently the case with many Post Office financial services, it is added.
Mr McFadden addressed the launch of the Post Bank Coalition in central London.
Afterwards, a Commercial Workers Union spokeswoman said the minister had been "very positive" about the future of the network.
However, she added: "He has totally missed the crucial element that it's not simply an extension of the current banking system that we want.
"He was very positive about banking, but he didn't realise how committed we are to having a system backed up by the government rather than a bank. So much has gone wrong with the banking sector and that's not what we want to continue."
Thousands of post offices have closed in recent years. Benefit payments are often paid directly into bank accounts and products such as car tax discs are increasingly sold online.
Despite £1.7bn in government subsidy designed to keep 11,500 branches open, there are fears that more will have to shut, particularly in rural areas.
Supporters of the Post Bank model want it to become a fully fledged alternative to commercial banks, serving more than 20 million customers every week.
They say that, even before the credit crunch, about three million people did not have basic bank accounts, with pensioners and those on low incomes most marginalised.
Efforts to give post offices more commercial freedom are backed by employers' groups who say small firms, whose access to credit has dried up, rely on a successful network to help their business.
"Most sub-post offices are run like small businesses and keeping the network alive by establishing Post Bank would not only retain jobs but could also, we estimate, create 11,000 new jobs," said John Wright, chairman of the Federation of Small Businesses.
Pensioners' groups said people had "lost faith" in High Street banks over the past year and a postal bank could provide "much-needed security" to those fearing for their savings.
With most of the 12,000 branches run by sub-postmasters or franchisees, there are questions over whether they have the expertise to expand in this way and how this will be funded.
The government says the Post Office is looking at new business opportunities to ensure it remains sustainable, such as being the sole provider for pictures for passports and ID cards.
Late last year the government awarded the contract to issue the Post Office Card Account - used by four million benefit claimants - to the Post Office amid fears that an extra 3,000 branches could close if it were contracted out.
Mr McFadden told BBC Radio 4's Today programme: "I think there's potential [in the ideas put forward]. There could be an expansion of banking products.
"Even though we don't have as many post offices as we used to, there are still more than all the banks put together."
Mr McFadden said: "There are different models of the Post Office expanding what they do in banking and postal services.
"I'm sure we can talk about what's best to be done. It's a trusted brand and it has a strong reach throughout the country.
"Perhaps it also reaches people who don't always go into conventional High Street banks."
Liberal Democrat small business spokeswoman Lorely Burt said: "With the credit crunch causing a loss of confidence in both banks and bankers, the time has never been better to create a Post Bank."