Cyprus has told the European authorities that it intends to apply for financial assistance, the fifth eurozone member to do so.
It said it needs help to shore up its banks, which are heavily exposed to the Greek economy.
The announcement came on another day of nervousness about the single currency.
Shares in Italy, Spain and Greece fell sharply amid concerns that an EU summit this week will again fail to produce a deal to shore up the euro.
The Spanish prime minister called for Thursday's European Union summit to "dispel doubts" about the euro.
The Italian and Spanish indexes both closed about 4% down. The fall on Spain's Ibex index was exacerbated by a Reuters report that the Moody's credit rating agency is planning to downgrade Spain's banks.
Earlier, Spain formally requested a bailout loan for its banking sector, expected to be for up to 100bn euros (£80.2bn, $125bn).
The country needs to find about 1.8bn euros over the next few days to recapitalise its second largest lender, Cyprus Popular Bank.
In a short statement, the government said that it required assistance following "negative spillover effects through its financial sector, due to its large exposure in the Greek economy".
A government spokesman, Stefanos Stefanou, said the amount of European aid would be subject to negotiations in the coming days.
He said that despite the request, the Cypriot government would continue negotiations for a possible loan from a country outside the EU, such as Russia or China.
The country has already borrowed 2.5bn euros from Russia, whose business people are important customers of Cyprus's relatively large offshore financial sector which offers low tax rates.
The BBC's chief economics correspondent Hugh Pym described Cyprus' problems as "classic contagion".
Its banks have lost large amounts on Greek government bonds. They are also facing big losses on loans made to businesses in Cyprus, which have been hard hit by the deep recession in neighbouring Greece, its biggest trading partner.
Credit ratings agency Fitch said the country, which has a population of one million, would need 4bn euros to support its banks, the equivalent of almost a quarter of its GDP, or economic output, last year.
Earlier, it cut the Cypriot government's credit rating to junk status, making it even harder for the country to raise the funds itself.
Fears are building that this week's two-day European Union summit could prove inconclusive.
"We must dispel doubts over the eurozone," said Spain's prime minister Mariano Rajoy.
"The single currency is, must be, irreversible," he said.
In another indication of the conflicts between European nations on the best way forward, Angela Merkel reiterated her opposition to calls to pool eurozone debt, which would make it cheaper for eurozone economies to borrow.
"There has to be a balance between guarantees and controls," she said.
IG Index analyst Chris Beauchamp blamed Chancellor Merkel's reluctance to share liability for eurozone debts for the share price falls.
"This was, is and will remain the fundamental issue in the crisis - Germany is understandably not keen on taking on the burden of debts built up by (as it sees it) spendthrift countries," he said.
The problems facing Europe's banks will be on the agenda at the summit of European leaders on 28 and 29 June.
The BBC's economics editor Stephanie Flanders said: "On difficult areas like banking union, officials are making more progress than anyone would have expected a month or two ago.
"But the Germans have succeeded in dramatically lowering expectations for what could be achieved by Friday."
Draft documents prepared for the meeting, which have been reported by news agencies, detail proposals for a single European banking supervisor and a common scheme for guaranteeing bank deposits.
There would also be a central fund to wind down bad banks.
Options for the regulator include having one body, possibly the European Central Bank, to oversee the continent's biggest banks, while another watchdog supervises the day-to-day operations of all the banks.
The proposals also include closer fiscal union, with the prospect of eurozone countries sharing debt raised again.