NEW YORK (CNNMoney) -- Leaders across Europe rushed to reassure nervous investors that they were working to keep Greece in the eurozone -- trying to head-off damage an exit would inflict on other troubled European countries.
On Tuesday, Greeks withdrew €800 million from Greek banks, and the threat of a banking panic heightened concern of a default and fear spilled into bond markets in Spain and Italy.
The first shot of good news came from the European Central Bank, which told CNNMoney Wednesday that it would continue to support Greek banks.
German Prime Minister Angela Merkel also lent support: "Europe needs to show solidarity and help, particularly with growth, unemployment and development," she said Wednesday.
The remarks helped ease the contagion threat across European markets, at least temporarily. But doubts about Greece's ability to pay its debts and stay in the eurozone remained high.
"With a cloud hanging over Greece's compliance with the terms of its latest credit line, EU governments may not agree to give the nation more cash," said Carl Weinberg, chief economist with High Frequency Economics, in a note Wednesday. "We remain wary of a potential for a hard default, literally at any time and without warning."
European leaders were careful to note that there would be limits to aid.
Mario Draghi, head of the European Central Bank, has repeatedly said that, unlike the U.S. Federal Reserve, the ECB cannot act as a "lender of last resort" to save Greece or any other country from default.
Merkel cautioned that the tough measures that have left some Greeks struggling to pay for food or utilities cannot be avoided. "It's very bitter, obviously [but] sacrifices had to be made," she said, adding, "These are necessary measures that had to be taken."
Greek voters rebelled against those harsh measures in the May 6 elections, denying the ruling coalition that had agreed to the bailout terms the votes they needed to form a new government.
With Greek voters set to go to the polls again June 17, the anti-austerity forces are expected to finish first, though their ability to form a ruling coalition remains uncertain.
Still, the fear is an anti-austerity ruling party could cause the bailout deal to unravel, leading to a Greek default and an exit from the euro.
It's unlikely that European leaders would agree to help Greece without austerity, since other troubled countries are, to a lesser degree, contending with the same issues.
"Ultimately I do not think the core countries will allow themselves to be 'held hostage' to Greek politics," said Elisabeth Afseth, fixed income analyst with Investec. "An exit will inevitably be messy and contagion is a very real issue, but avoiding it may make it very difficult to continue fiscal and economic reforms in the rest of Europe if Greece is seen to get special treatment."
Greece's borrowing costs retreated slightly but remain near record highs, with the yield on the Greek 10-year bond hovering around just under 29%.
The borrowing costs in Italy and Spain -- the two largest nations facing their own sovereign debt worries -- remained high, with yields on 10-year bonds near the 6% mark, considered the first warning sign of a potential need for a bailout.
While Spanish Prime Minister Mariano Rajoy threw his support behind Greece, he also said, "All of us have to live up to our commitments."
Germany and France held debt auctions Wednesday that drew strong demand, pushing Germany's 10-year yield as low as 1.47%.
|What we want Apple to unveil at WWDC|
|Millennials squeezed out of buying a home|
|7 traits the rich have in common|
|Big Data knows you're sick, tired and depressed|
|Your car is a giant computer - and it can be hacked|
|Overnight Avg Rate||Latest||Change||Last Week|
|30 yr fixed||3.98%||4.08%|
|15 yr fixed||3.09%||3.11%|
|30 yr refi||4.06%||4.16%|
|15 yr refi||3.17%||3.20%|
Today's featured rates: