* Benchmark euro Libor rates edge higher, dollar steady
* Market tensions ease, but banks still hoard cash
* 1-month U.S. T-bill rates down from last week (Adds economist's quote, changes dateline)
By Chris Reese and Kirsten Donovan
NEW YORK/LONDON, June 1 (Reuters) - Benchmark euro interbank lending rates edged higher on Tuesday and dollar rates were steady as money market tensions eased from elevated levels but banks continued to hoard what funds they could get.
Money markets had appeared pressured over the last couple of weeks -- illustrated by a scramble for dollar funds -- over fears that international lenders were becoming reluctant to invest in the euro zone as a sovereign debt crisis there spiraled.
One key indicator of stress, the forward September 3-month Libor/OIS spread fell to around 60 basis points, according to ICAP data, from around 68 basis points a week ago, while the three-month euro/dollar cross currency swap was at -55 basis points from its recent lows of -70 basis points ICAB4.
But analysts said there was still a reluctance to lend dollars to many European banks.
"It's looking healthier than this time last week, but Europe is still very much left on the top shelf," said a dollar trader.
Banks were paying around 1 percent to swap euros into dollars, the trader said, well above Tuesday's benchmark dollar Libor fixing USD3MFSR= of 0.53625 percent, but still around quarter of a percent below rates currently being charged by the European Central Bank's and Federal Reserve's swap facility.
Dollar Libor has been rising steadily since early March along with worries over the outcome of the euro zone debt crisis. Late last week the fixing reached a recent high of 0.53844, which was the loftiest in nearly a year.
"Funding pressures are escalating again in the global banking sector as contagion risks intensify," said David Rosenberg, chief economist and strategist at money management firm Gluskin Scheff in Toronto.
The desire for safe-haven, short-term U.S. debt on Tuesday pressured one-month Treasury bill rates lower, down to 0.147 percent from 0.157 percent late on Friday, according to Reuters data. U.S. markets were closed on Monday for the Memorial Day holiday.
Relative calm toward the end of last week allowed a cautious reopening of credit markets for banks raising funds, with Deutsche Bank launching the first senior bank deal since April 15.
European banks continue to hoard cash however, with around 280 billion euros of excess liquidity in the system and overnight deposits at the ECB hitting record highs on Friday.
Banks took almost 118 billion euros at the ECB's regular one-week tender on Tuesday, up from a maturing amount of 106 billion euros [ID:nECB000014], the sixth week the amount has risen, Morgan Stanley said.
The ECB on Monday acknowledged in a report that euro zone debt tensions may force it to delay a phasing-out of cheap lending operations designed to help banks through the financial crisis. [ID:nLDE64U0OS]
It also warned that euro zone banks face up to 195 billion euros in a "second wave" of potential loan losses over the next 18 months due to the financial crisis.
"The problems in the banking sector and the anticipation of write-downs are not new," said Societe Generale economist James Nixon. "But in the current environment it is not helpful to be reminded of these problems."
Benchmark euro Libor rates EUR3MFSR= were a third of a basis point higher at 0.63688 percent. (Editing by Kenneth Barry)