European Union finance ministers held their first discussions about a European Commission proposal to set up a single eurozone banking supervisor on Friday – but major disagreements are already threatening to dash hopes of approval in December.

The controversial plan has raised fears among non-eurozone countries that they will lose influence over EU-wide banking regulation.

Germany has said that it believes the European Central Bank (ECB), which will take on the supervisory role, should not oversee all 6,000 eurozone banks, as has been proposed by the Commission, but only larger, systemically important institutions – a move that would put it at odds with other eurozone countries and the UK.

At their meeting on Friday afternoon in Nicosia, EU finance ministers were presented with a report on banking union by the Brussels-based think-tank Bruegel and they will continue their discussions on Saturday.

Michel Barnier, the European commissioner for the internal market, who is leading work on the draft legislation, attempted to play down ministers’ fears.

He said non-eurozone countries should not be worried about the plans. “I will not allow the single market to break down,” he said after Friday’s meeting. “Regulation will remain at 27 [EU member states].”

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He added that other steps, such as a common bank resolution fund, would only be part of a “step by step approach”.

The European Parliament is also expected to raise concerns about the banking union plan, particularly the perceived threat to the single market.

While the UK supports the role of the ECB as eurozone banking supervisor, it is concerned about the repercussions of a two-tier system.

British finance ministry officials will say that they will support the plan only if safeguards are put in place to protect the single market.

Under the plans, there will be changes to the way the EBA votes on cross-border banking disputes that will make it harder for member states to get their own way. The UK and several other non-eurozone countries fear it could give the ECB too much sway over decisions.

The Bruegel paper said that a banking union needed “a common supervisor and common resolution arrangements with the aim of reducing fiscal costs. At the same time, arrangements for a common fiscal backstop need to be made.”