Spain is warning that Europe's single currency will unravel unless its leaders decide within weeks to centralise budget and tax policies in the eurozone and agree on a strategy to pool responsibility for failing banks.

As Spain's prime minister, Mariano Rajoy, came under mounting international pressure to accept the eurozone's fourth national bailout in two years, the government in Madrid angrily rejected the demands, insisting that it did not need rescuing. With fears of a euro meltdown having rapidly shifted from Greece to Spain, Rajoy is pleading for a direct eurozone rescue of his country's banks, to avoid the humiliation attached to requesting a national bailout.

Sources familiar with the Spanish government's thinking said its negotiating position was that the fundamental quandary facing the eurozone was not Spain, but a European failure of leadership in persuading the financial markets that the euro would be defended at all costs.

A Brussels summit at the end of the month would have to remedy that by agreeing to establish a eurozone banking and fiscal union – major federalising steps certain to be fought over. Without that commitment, Spain fears the single currency would be finished in months.

The Spanish government believes that the eurozone's fourth-biggest economy is too big to rescue and that the consequences of abandoning Spain to the markets without a pledge of major European reform could be so ferocious that the single currency would not survive.

The current rules governing eurozone bailouts stipulate that a government has to request help and that the money may only be channelled via governments – increasing the national debt burden.

But Spain is stalling until key euro group meetings, the G20 summit and the Greek election later this month. Some analysts believe that if Spain is finally forced to request a full-scale EU/IMF bailout it is likely to come around 20 June.

Sources in Brussels confirmed that a rescue plan was being hatched for Spain – but it could be limited to desperately-needed banking aid, rather than a full national bailout.

Luis de Guindos, the Spanish finance minister, said his government would wait until the results of an independent audit of Spanish banks was completed later this month before pondering its options.

The IMF is to deliver its verdict on the condition of the Spanish banks on Monday, followed a week later by the Spanish audit. "From that basis, the Spanish government will decide what measures must be taken to recapitalise banks," said De Guindos. Madrid was joined by Washington and London in calling on the eurozone, principally Angela Merkel, the German chancellor, to deliver a persuasive new plan quickly for saving the euro. They fear the crisis might inflict immense damage on the US and UK economies.

A big move towards reform could immediately ease market pressure on Spain's borrowing costs, though the European Central Bank might still have to supply some funding while details of the new union were thrashed out.

Sources familiar with the Spanish government's thinking believe the country's banking crisis could be fixed much more cheaply than the €50bn bill currently estimated by analysts. In Brussels the signs are that a deal is being considered that would be more palatable for Rajoy by explicitly linking the rescue money to the banking problem and not to his government's stewardship of Spain's finances.

As the ECB left eurozone interest rates unchanged at 1%, ignoring calls for a slight reduction, its head, Mario Draghi, dismissed the criticism from Washington and London – but he also urged eurozone leaders get their act together.

Berlin is pushing the fiscal union, but on its own terms. It wants to force common rules and targets but avoid any early commitment to sharing liability for the debt or bank savings of individual countries. David Cameron is to go to Berlin on Thursdayto try to push Merkel into a more protective stance on the euro, which would entail German pledges to underwrite struggling countries' debt. Following a telephone conversation with Barack Obama, the British prime minister will tell Merkel the US and the UK are insisting on "an immediate plan" on the euro, Downing Street said. The prime minister will tell Merkel the eurozone has no more than weeks to act to shore up the single currency.

Cameron's spokeswoman said the pair "agreed on the need for an immediate plan to tackle the crisis and to restore market confidence". Cameron's regular interventions from the sidelines of the euro crisis irritate Berlin and Brussels and Merkel is unlikely to be swayed, although Germany is showing some signs of greater flexibility.

The White House, fearing the impact of a European disaster on Barack Obama's re-election campaign, is becoming more trenchant in its criticism of the eurozone and its demands of the Germans.

In Brussels, the signs are that the sides were inching towards a deal that would be made more palatable for Rajoy by explicitly linking the rescue money solely to the banking problem - and not to his government's stewardship of Spain's public finances.

German politicians dropped any pretence that they were not pressing Rajoy to ask for a bailout, but said the rescue could come without very tight strings attached. "I do think that Spain has to come under the rescue shield," said Volker Kauder, the parliamentary leader of Merkel's Christian Democrats in Berlin. "Not because of the country, but because of the banks."

Tristan Cooper, sovereign credit analyst at Fidelity Worldwide Investment said: "The willingness to support Spain is there. The difficulty is designing a method that can satisfy Germany and the market.

Although sick banks are Spain's most acute ailment, there are more chronic ones. These include the highest unemployment and the third widest fiscal deficit in Europe in a deep recession.

Markets would react positively to an adequate bank recap solution. A structural change in investor sentiment requires the prospect of a sustainable economic recovery and a credible plan for achieving it."

The expectation is that any decisions will be delayed until after the Greek election on 17 June. Eurozone finance ministers are to meet on 21 June. The next day Rajoy is due in Rome for a summit with the leaders of Germany, France, and Italy before the Brussels summit a week later.

If the result of this risky round of brinkmanship and bargaining is an agreed "road-map" towards the medium-term aim of a eurozone federation, the Spanish hope the heat will be off, pressure from the financial markets will subside, their borrowing costs will sink and recapitalising their banking sector will become more feasible.