Banks including BNP Paribas and ING are ditching billions of euros of euro zone government bonds, cutting their exposure to the region's trouble spots.

More lenders are expected to retreat as the euro zone crisis deepens and leaders raise the possibility of the exit of Greece from the bloc, further damaging prices.

The market value of the debt of the countries most under scrutiny is likely to decline further as banks unload sovereign bonds, Charles Dallara, managing director of the Institute of International Finance, warned on Wednesday.

BNP, the biggest overseas private holder of Greek government debt, took a 2.6 billion euro (2.4 billion pound) writedown on Thursday as the crisis in the currency bloc deepened, mostly because it wrote down the value of its Greek bonds to 40 percent of par value.

The bank had been told by the French government not to sell down its Greek bonds as the country's troubles grew over the summer, to prevent destabilising the euro zone, a senior banking source has told Reuters, on condition of anonymity.

BNP lost 362 million euros in the third quarter and said it will lose another 450 million euros in October from selling almost 25 billion euros of sovereign debt, or a quarter of its holdings, reducing its Italian bonds by 8.2 billion euros to 12.6 billion euros over the four months.

The retreat is not restricted to those economies seen as most vulnerable to the crisis.

In addition to cutting back on 2.2 billion euros of Spanish sovereign bonds (leaving 0.5 billion euros), BNP also reduced its French debt holding by 1 billion euros (leaving 13.8 billion euros) and its German debt by 1.4 billion euros (leaving 2.5 billion euros).

In a similar move, Dutch financial group ING said it had cut its Greek, Italian, Irish, Portuguese and Spanish sovereign bond holdings by 5.4 billion euros, also in the last four months.

TOUGHER RULES

The IIF, which represents over 450 financial firms, half of them in Europe, said in a letter to G20 leaders ahead of their summit in France that the sales of government bonds were the result of banks being hit by tougher capital and liquidity rules -- including their increasingly questionable emphasis on sovereign debt.

Regulators have encouraged banks since the 2007/08 financial crisis to increase their holdings of liquid assets such as government bonds and cash, so they could withstand at least a 30-day funding crisis.

The European Central Bank is likely to be by far the biggest buyer of the bonds being offloaded, although BNP said all its sales of Italian debt had been on the market and not to the ECB.

The ECB has bought 100 billion euros of bonds since August after it reactivated the controversial programme -- - known as the Securities Markets Programme -- which aims to keep borrowing costs in check. It bought 4 billion euros last week.

The ECB does not break down its purchases, but most purchases since August are expected to have been of Italian and Spanish debt.

Hedge funds or other opportunistic investment firms could also be buyers, although this week's collapse of U.S. firm MF Global after big bets on the euro zone may deter many.

Probably the main buyer is the ECB's SMP program ... but the second largest buyers would be domestic insurers and pension funds, said Andrew Fraser, investment director for fixed income at Standard Life Investments.

As they receive coupon payments or as bonds mature, they have to reinvest that money in domestic bonds because the liability is in the domestic market.

Other banks to cut holdings include Barclays, which last week said its sovereign exposure to Spain, Italy, Portugal Ireland and Greece (PIIGS) fell by 31 percent in the third quarter to 8 billion euros.

Deutsche Bank said its net exposure to sovereign PIIGS debt increased slightly in the third quarter mainly due to trading book positions. But its end-September holding of 4.4 billion euros was down from 12.1 billion euros at the start of the year, with its Italian holdings almost halving to 4.4 billion euros.

Royal Bank of Scotland could take a 180 million pound hit on its Greek bonds if it marks them to current prices when it reports on Friday, despite taking a conservative 50 percent loss on them in August.

BNP's residual exposure to Greek sovereign bonds was now 1.6 billion euros. It said a deal whereby private sector investors will voluntarily lose half the nominal value of their Greek bonds was still shrouded by uncertainty.

ING took a 467 million euros hit as it marked its Greek government bonds to market value, which is currently around a 63 percent loss.

(Additional reporting by Sinead Cruise, Sarah White, Edward Taylor and Gilbert Kreijger; Editing by Alexander Smith and Helen Massy-Beresford)