The record rise of the euro against the dollar and sterling has sparked fears that it could push eurozone countries into deflation.
Economists are now urging the European Central Bank (ECB) to cut interest rates when it meets on 5 June.
The euro hit its highest ever level against the dollar on Tuesday, reaching $1.193 - surpassing its previous peak, reached shortly after the single currency's launch in January 1999.
By about 1500 GMT on Wednesday, it had fallen back to $1.176 but economists warned that unless the ECB cuts rates, the euro's rise will continue.
"We could be faced with a real problem here," Andre de Klerk, a European currency expert at ECU Group, told the BBC's World Business Report.
A strong euro will make European exports more expensive, and will favour the sale of cheaper US goods abroad.
There are also fears it could lead to deflation in key European economies.
Mr de Klerk said he was concerned about Germany, Europe's largest economy.
"It is a key player in the eurozone and has a huge impact on other countries, like Switzerland," he said.
"If this spreads, it will be much harder to contain it than to take steps to prevent it now."
His comments came as the Finnish newspaper Kauppalehti quoted the ECB's chief economist Otmar Issing admitting deflation was a possibility.
"If we are speaking of individual countries, like Germany, no one can rule out the possibility that with the currently low inflation growth at some point the zero barrier will also be broken," Mr Issing told the paper.
Many economists have suggested a rate cut of between a quarter and half a percentage point is on the cards for next week.
Its failure to take action so far has prompted criticism from some circles.
"They should do, everyone knows that," Mr de Klerk told the BBC.
"Even a 100 basis point cut would suffice."
Analysts said the rise in the euro had been caused in part by demand for eurozone government bonds but also a lack of objection to the euro's rise by the European Central Bank (ECB).
"If you take into account the balance of statements from ECB officials, it's very much in favour of the current level of the euro, and that's giving support to investors to buy it on dips," said Paul Mackel, a currency strategist at Dresdner Kleinwort Wasserstein.
Rate cut talk
The euro has also been underpinned by recent signs that the US government may be relaxing its traditional commitment to a strong dollar in an effort at kick-starting an export-led recovery.
The eurozone's higher interest rate - at 2.5% compared with just 1.25% in the US - has given investors an added incentive to hold euros rather than dollars.
The single currency's rise has been checked slightly by reports that the ECB may be preparing the ground for an interest rate cut.
However, analysts said similar action by the US Federal Reserve could leave the long-term situation unchanged.
"If you take into account that the Fed is expected to do
the same a few weeks later, then the net effect is really zero," Mr Mackel said.