The financial institutions have been accused of operating a culture of aggression and threat against their business customers - a charge the banks reject.
But the clerics say they are "holding back the recovery and putting companies and their employers at risk".
Church of Ireland Archbishop Alan Harper, Roman Catholic Cardinal Sean Brady, President of the Methodist Church the Rev Paul Kingston and Presbyterian Moderator Dr Norman Hamilton want to meet the banks.
Archbishop Harper said: "There is a culture of aggression and threat where the only priorities are the banks' priorities."
The churchmen are concerned about significant inflation in interest rates and transaction charges; immediate withdrawal of overdrafts; the inaccessibility of decision makers; micro-management of a business's affairs and discrimination against areas like construction.
"It is becoming clear that there is a tangible risk to the economy through banks seeking too rapid a restoration of their own balance sheets," Archbishop Harper added.
"That risk translates into a threat to jobs and family income for the rest of us, inflicting additional misery on businesses and their employees."
He said the experience of some businesses was shocking, causing immense pressure and threatening closure and job losses.
Cardinal Brady said: "Many of those who have come to us for support have been placed under needless financial pressure when they are running solid businesses which have provided much-needed employment across Northern Ireland."
Mr Hamilton added: "At a time when Northern Ireland, through the efforts of its own politicians, local business people and entrepreneurs, is trying to strengthen and build the economy, it is ironic that many of the financial decisions needed to support it are being taken by people from elsewhere."
'Worry'
One shop owner told UTV of his concerns - but wished to remain anonymous for fear the banks would take action against him for speaking out.
"I need the bank to be more open and I need the banks to be more clear in their message," he said.
"They communicate in writing with one message and when you sit round a table, they'll agree to another so they would put people into positions where they can't sleep at night. And become very difficult and they go home and they worry. It is not necessary."
Despite having a turnover of £7m, the businessman received a letter from the bank two months ago, threatening to withdraw his overdraft facility - a facility which he needs to survive.
"If the banks pull their overdraft facility - which they have threatened to do - it would mean us having to close the business with the result of a loss of 125 jobs because we employ 125 people in the area.
"We are local to the economy and we have been for the last ten years.
"The first sign of a downturn, the banks need to be supportive and not be a threat and take away our overdraft because that leaves us in a very difficult position to trade. We have never faulted on our overdraft facility - we have always paid the interest which makes it all the more unreasonable for to look to withdraw it."
He added: "Every business is different and every business individual and I think there has to be political pressure from a much higher level to the banks to make them understand what is going on."
'Unacceptable'
Gordon Best, regional director of the Quarry Products Association in Northern Ireland, said it was unacceptable how some financial institutions saved by public money were treating long-standing businesses.
Ulster Bank said it had already agreed to meet Archbishop Harper and other church leaders to discuss their concerns.
A statement added: "Ulster Bank is committed to working closely with our customers to help ensure the continued success of viable businesses."
In 2009, Ulster Bank provided more than £290m to around 1,000 small businesses and the bank is committed to lend £300m to small businesses this year.
"Ulster Bank provided 80% of all lending by Northern Ireland banks through the enterprise finance guarantee (EFG) scheme, which was set up by the UK Government to support small firms at the margins of commercial lending decisions."
A spokesman for the British Bankers' Association said: "Bank lending is not risk finance: it is debt finance. It is not the banks' money to risk; it is their customers.
"Therefore banks need borrowers to assure them they have a robust plan in place to ensure the money is repaid and will work with them to achieve this.
"The coalition of churches understands it has not yet taken account of the banks' perspective, and has invited the banks to meet with them to discuss the issues their parishioners raise.
"The British Bankers' Association looks forward to meeting with them and discussing their concerns in detail."