* Cyprus bank bailout bill rises
* Largest lender says needs capital support
* Island's two largest banks need to plug shortfall
* Finland says will want collateral
NICOSIA, June 27 (Reuters) - The cost of Cyprus's EU bailout to support a major bank jumped unexpectedly on Wednesday after the island's largest lender said it too needed state support to meet a regulatory shortfall in capital by June 30.
The tiny Mediterranean island became the fifth euro zone nation on Monday to seek emergency funding from Europe, with a bailout bill that could potentially amount to more than half the size of its economy.
Cyprus already needs 1.8 billion euros ($2.2 billion) to help recapitalise Popular Bank, its second-largest lender.
Bank of Cyprus followed with a call for aid on Wednesday, saying it would need "temporary capital support" from the state to the tune of about 500 million euros - effectively jacking up the nation's exposure to its banks to 2.3 billion euros.
Cyprus banks have been crushed by a writedown on Greek sovereign bonds negotiated in an attempt to make Greece's debt mountain more sustainable. Bank of Cyprus and Popular recorded record losses in 2011, depleting their regulatory capital.
Combined, a 2.3 billion euro figure is a considerable chunk of Cyprus's 17.3 billion euro economy, and two euro zone sources on Tuesday put a potential bailout amount at up to 10 billion euros.
The government says no amounts have been discussed. Officials from the ECB, which will carry out an assessment with the European Commission of precisely how much aid Cyprus may require, were due on the island on Monday, two sources said.
It was unclear whether the International Monetary Fund, which already has a team in Cyprus on a previously-scheduled and unrelated mission, would get involved.
Although a 10 billion euro figure would easily be within the firepower of the European Financial Stability Facility (EFSF), it could lead to calls for collateral.
Finland will demand collateral for its share in rescuing Cyprus, if the EFSF is used, Prime Minister Jyrki Katainen said on Wednesday.
"If the non permanent fund is used to aid Cyprus, then yes, Finland will demand collateral," Katainen told reporters.
"In Finland's view... over some time span it could prove wise for larger European banks to have a crisis fund, which the banks would gather themselves."
Cyprus kept markets guessing for weeks as to whether it would seek aid from its EU partners or resort to bilateral lending, an option which remains open and one which would supplement a bailout.
One fear in Nicosia is pressure that its low-tax status could be challenged, and unpopular austerity measures imposed with a general election in eight months.
Cypriot finance minister Vassos Shiarly said any speculation on bailout conditions was premature.
"I believe what we will discuss and conclude on won't be so painful as some may believe," he told state radio.