The argument is between some banks and independent cash machine providers.
Members of Link, operator of the UK's cash machine network which connects the country's 70,000 cash machines, met last week to discuss its business model.
Banks currently pay cash machine providers around 25p per transaction, according to The Independent.
But some banks say the charges are too high and have demanded a reduction.
The ATM Industry Association trade body said one third of its machines would have to charge or be removed if charges were lowered.
Andrew Tyrie MP, chairman of the House of Commons Treasury Committee, said the situation could be investigated unless it was resolved.
Widespread charging would be of considerable concern, he said, particularly in rural areas and poorer urban neighbourhoods.
Link chief executive John Howells acknowledged that some "commercial perspectives" may vary but added that consumer needs were top priority.
"Every LINK member was clear at the meeting that ensuring the future of the LINK Network and the cash access needs of UK consumers remains their number one priority.
"It was agreed that a working group of members will be established in order to explore a way forward for the sustainability of the LINK Scheme, particularly LINK Interchange.
"Details of this group will be defined as soon as practical and it is anticipated that this group will report back to the LINK Network Members Council later in the year.
LINK would continue to work closely with its 39 members to keep regulators, government and consumer groups fully informed of the situation, said Mr Howells.
The LINK network was continuing to operate normally and it was business as usual for consumers at all the UK's 70,000 ATMs, he added.
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