* Italy seeking to bail out two regional lenders
* Nouy seeks greater discretion in capital demands (Adds detail, quotes)
By Francesco Canepa and Balazs Koranyi
FRANKFURT, March 23 (Reuters) - Some euro zone banks may need to be shut if they become unviable, the European Central Bank's top supervisor said on Thursday, as the Italian government seeks to bail out two regional lenders.
Daniele Nouy, the head of the ECB's supervisory arm, told the European Parliament there were too many banks in the euro zone and called for Frankfurt to be given greater discretion when deciding how much capital they must hold.
As the euro zone's top bank supervisor, the ECB will have to decide whether Banca Popolare di Vicenza and Veneto Banca are solvent and how much capital they need, as it did with their larger peer Monte Paschi late last year, if Italy's planned rescue is given a preliminary green light.
Nouy did not name any bank or country but stressed European rules allowed for some banks to be shut down.
"In specific cases consolidation may also take the form of the unwinding of banks if they become unviable," she told a parliamentary committee.
Nouy said she welcomed the European Commission's new proposed rules on bank capital, which introduce several tweaks to globally agreed standards.
But she warned they constrained supervisors' powers, particularly when it comes to set capital requirements, known in the industry as Pillar 2.
"Most prominently, the proposal may frame supervisory action too tightly," Nouy said.
"It does so by constraining the flexibility required by the supervisor in taking action in cases not foreseen in the legislation and in determining the composition of the Pillar 2 capital requirements."
Specifically, she said supervisors should be able to demand that their requirements be met with Core Tier 1 capital, such as equity, and to impose individual deductions, provisions or filters to specific banks.
She also said deviations from global rules made banks more vulnerable and difficult to compare for investors, while the Commission's proposal did not go far enough in making rules more homogeneous across Europe. (Reporting By Francesco Canepa; Editing by Balazs Koranyi and Gareth Jones)