By Kirsten Donovan LONDON, Nov 23 (Reuters) - Euro zone banks borrowed only a modest amount of dollars from the European Central Bank on Wednesday but mounting funding stresses may see that change at a three-month tender in early December. Demand for dollar funding held steady with just two banks taking around $550 million in one-week funds, despite market costs of raising dollars standing at painfully elevated levels. By contrast, euro zone banks increased their euro borrowing from the ECB to the highest level in two years on Tuesday. U.S. money funds reduced dollar loans to European banks by an additional 9 percent in October, Fitch Ratings said in a report on Tuesday. The funds have cut lending to Europe by 42 percent since the end of May. However, it is still around 30 basis points cheaper for euro zone banks to borrow dollars in the market for one week than from the ECB, RBS said. However, the bank added that if financing stress intensified, there may be higher demand at a three-month dollar tender in early December. The three-month cross currency basis swap, which measures the cost of swapping euros into dollars, is at its most expensive level since the 2008 financial crash, at around 140 basis points. "If we continue to see funding stress staying as wide as it now, so beyond the 130 basis point level, we could see an allotment of up to $4 or $5 billion," said RBS rate strategist Simon Peck. "If dollar funding conditions continue to deteriorate, for example beyond 150 basis points in three-month cross currency basis, perhaps we'll see $5 or 10 billion or more but the focus is now on any rhetoric or any move to cut the rate charged." Banks borrowed just $395 million in a three-month tender at the beginning of November and $1.35 billion in October. Many banks are not only shut out of money markets but are also finding longer-term financing markets closed for business as fears over exposure to euro zone sovereign debt erodes what little trust had been built back up after the 2008 crisis. The spread of senior bank bonds in the secondary market over mid-swaps has marched relentlessly higher with those of France's BNP Paribas, for example, rising to 220 bps, compared with 130 bps in August, and Italy's UniCredit's more than doubling to 750 bps from 325 bps, according to Societe Generale. Raising new financing would probably cost an institution even more if it could access the market. Only 11 billion euros of senior paper has been issued since the beginning of July. Any further slow-down in lending to banks or rise in their cost of borrowing will add to pressures on the euro zone economy as institutions seek to deleverage, said Societe Generale credit strategist Suki Mann. "Banks will preserve their own liquidity," he said. "They'll reduce the amount of lending they do, compounding the uncertainty that we have and exacerbating the slowdown in the economy." Data on Wednesday showed the region's private sector contracted for a third month in November as the debt crisis dragged the currency bloc to the brink of recession. Markets are expecting the ECB to cut interest rates again early next year.

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