(REUTERS) - Standard & Poor's said on Tuesday it is considering downgrading the European Financial Stability Facility, the Eurozone's bailout fund that is financed by member governments, after saying it could downgrade the majority of Eurozone nations on Monday.

The EFSF could be downgraded by one or two notches, and the lower rating would depend on whether the six triple-A rated nations in the Eurozone are cut.

(Reporting By David Gaffen, Editing by Chizu Nomiyama)