* Euro stays near last week's low just below $1.25
* Doubts grow that Spain can support ailing banks on its own
* Eyes on whether Spanish govt bond yield hits 7 pct
* EUR short covering may be curbed ahead of Irish referendum
By Jessica Mortimer
LONDON, May 29 (Reuters) - The euro edged up against the dollar on Tuesday as investors cut hefty bearish bets in the currency, but worries about Spain's banking sector left it hovering close to its lowest levels in nearly two years.
Analysts and traders said the euro had good support at the $1.2500 level and Friday's trough of $1.2495, with bids around that area, but expected it would soon break lower given the extent of the concerns surrounding the euro zone debt crisis.
Worries about the cost of shoring up Spain's banking system lifted its debt yields on Monday, driving the gap between Spanish and German 10-year yields to euro era highs, as the risk grew that Spain may be forced to seek an international bailout.
The euro was up 0.2 percent at $1.2566, with traders citing demand from corporates and Middle East names.
Having failed to clear resistance at previous support around $1.2625 for three days in a row, however, the euro was vulnerable to another test of Friday's low, which marked its weakest since July 2010.
"We may see a bit of consolidation here but going forward we still have a euro that is very weak and vulnerable. The widening of spreads between Spain and Germany and Italy and Germany keeps worries about the debt crisis very much alive," said Niels Christensen, currency strategist at Nordea in Copenhagen.
"I don't see the euro moving above $1.27. It's only a matter of time before it breaks $1.25. This is psychological support but it's not a big level like the January low was (around $1.2624) and that has clearly broken."
The euro gave up most of the gains made on Monday after Greek polls showed more support for pro-bailout parties ahead of the country's election on June 17. That eased fears Greece may leave the euro zone.
Bids just below $1.25 may support the euro for now, though further losses could see it drop towards $1.2450, where traders reported stop-loss sell orders.
"Although pessimism over Greece is somewhat receding, worries about Spain are growing, with markets watching whether the Spanish bond yield will hit the seven percent mark," said Masafumi Yamamoto, chief FX strategist at Barclays in Tokyo.
Short-term, the euro may continue to be held up by bouts of short covering. Speculators bolstered short euro positions to record highs in the week ended May 22, leaving ample scope for a correction as they cut positions and book profits.
TROUBLES IN SPAIN
Many traders expect further downside in the euro as they fear troubles at Spanish banks hit by a bust in property could further complicate Madrid's efforts to rein in its debt.
Spain's fourth-largest lender Bankia has asked for a bailout of 19 billion euros, in addition to 4.5 billion euros the state has already pumped in to cover possible losses on repossessed property, loans and investments.
Prime Minister Mariano Rajoy on Monday again ruled out seeking outside aid to revive Spain's banking sector, though many investors are sceptical this will be possible.
Spanish 10-year bond yields rose above 6.5 percent on Monday. A level of 7 percent is seen as critical as euro zone countries that have previously requested bailouts did so soon after their 10-year yields rose above that mark.
Any buying in the euro may also be curbed ahead of Ireland's referendum on Europe's new fiscal treaty on Thursday, although the market is cautiously optimistic that the Irish will support the treaty on fear that a "no" vote could add fuel to the fire.
Against the yen, the common currency fetched 99.87 yen , not far from a four-month low of 99.37 yen hit last week. The yen, along with the dollar, was supported by the market's risk averse mood.
The dollar stood at 79.47 yen, not far from a three-month low of 79.002 yen.
The higher-yielding Australian dollar was up 0.4 percent at $0.9888, above last week's six-month low of $0.9690.