Billionaire investor Wilbur Ross, who is a major shareholder in Greece's Eurobank, said that diluting shareholders of the banks in their upcoming recapitalization could turn off private investor interest in the lenders.

"In view of the volatility of politics in Greece, investors will not be comfortable with committing new equity capital to banks that are effectively nationalized," Ross, chairman and chief strategy officer of WL Ross investment company, said in a statement.

He said this applies particularly in the case of Eurobank, the only one of the four big banks that is majority owned by the private sector.

"In view of how well Eurobank performed in the ECB analysis, there is clearly no justification to interfering with its management or governance," he said.

The ECB's health check showed that Eurobank, which is 35.4 percent owned by Greece's bank bailout fund HFSF, needs to cover a capital shortfall of 2.12 billion euros - the lowest among the four lenders,

"Since it was the actions of the government that caused the imposition of capital controls and since these in turn have led to the need for equity, it would be nonsensical for the government now to dilute shareholders at share prices that are a small fraction of the underlying value," he said.

"Doing so will endanger the success of the private sector financing and reduce the likelihood of investor participation in the forthcoming privatizations."