The European Central Bank remains firmly opposed to any restructuring of its Greek bond holdings as the debt was acquired for monetary policy purposes, according to two people familiar with the Governing Council's stance.

While the ECB faces pressure to join private-sector investors in taking losses on Greek debt, the central bank sees this as potentially damaging to confidence in the institution if it were to take part, said the people, who declined to be identified because the matter is confidential.

International Monetary Fund Managing Director Christine Lagarde said today that European governments and other public holders of Greek debt may have to increase support if private creditors don't go far enough. Investors and European finance ministers remain at odds over how much private investors should shoulder in the Greek bailout.