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Another week, another euro drubbing...

Euro-dollar parity in 'a few trading sessions?'

The plunge in the euro may be starting to look overstretched, but that's unlikely to stop traders from pushing the battered single currency even lower this week, analysts warned.

The euro briefly fell to a fresh 12-year low against the dollar Monday, at about $1.0457, before recovering a touch. Last week, the currency slid 3.2 percent -- its biggest weekly fall since 2011 -- as the European Central Bank embarked on a 1-trillion-euro quantitative easing program and talk of a rate rise by the U.S. Federal Reserve this year grew.

"The euro continues to track lower and while it continues to struggle above the $1.0600 level, the prospect of a move to parity remains very much a possibility," Michael Hewson, chief market analyst at CMC Markets, said in a note.

"The move lower continues to get more and more overextended, yet new lows continue to be hit every day."

Read More Weak euro, ECB stimulus make Europe a solid bet: Wisdom Tree

Stoyan Nenov | Reuters

Market positioning data from the Commodity Futures Trading Commission on Friday showed that long dollar bets, which reflect the view that the greenback will strengthen, rose to their highest level in four weeks in the week ended March 10.

The value of the dollar's net long position was $44.31 billion that week, compared with $40.85 billion the week before. It marked the eleventh straight week that long positions on the greenback have been in the $40-billion region.

Michael Every, head of financial markets research for Asia-Pacific at Rabobank, told CNBC Asia's "Squawk Box" that the euro could hit parity, or one-to-one against the dollar, within a matter of trading sessions.

"We've seen an incredible swing towards the dollar and away from the euro, and if we do get the removal of the word 'patience' from the Fed on Wednesday and weak euro zone data we could get there (parity) in a week," he said.

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Every was referring to this week's Federal Reserve meeting and speculation that the central bank could remove the word "patience" from its guidance about the pace at which it will normalize monetary policy. If it does, it could signify that rates could rise this year.

Saktiandi Supaat, head of global FX strategy at Maybank, told CNBC that the euro could test resistance levels of $1.02 over the next week, which would imply a further loss of 3 percent from current levels. The euro has tumbled almost 25 percent over the past year.

Some analysts said that even if the Fed does not use the word "patience" this week, it could still signal that a rate rise as early as June may not be on the cards – something that could knock the resurgent dollar and give the euro a lift.

"The euro is oversold at these levels and this is a good week for a bounce. I think the Fed will be cautious and temper expectations for a rate rise in June," Boris Schlossberg, managing director of FX strategy at BK Asset Management in New York, told CNBC Europe.

"The Fed is the only major central bank looking to tighten and it is hard to do that when most central banks are still easing," he added. "I think the markets are getting a bit ahead of themselves in terms of dollar strength."

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