Crude-oil futures fell in Asian trade Monday with the U.S. oil benchmark dropping to its lowest level in more than 5 1/2 years as financial markets reeled in the wake of Greece's elections.

Oil traders were cautious after Greek leftist party Syriza won Sunday's vote, pushing the euro to its lowest levels in more than a decade against the U.S. dollar and Japanese yen in Asia trade.

A steady appreciation in the U.S. dollar has weighed across prices of commodities, especially oil, which is dollar-denominated.

On the New York Mercantile Exchange, light, sweet crude futures for delivery in March traded at $45.03 a barrel at 0419 GMT, down $0.56 in the Globex electronic session. It had fallen to as low as $45.35 a barrel, but pared some early losses.

Brent crude for March delivery fell $0.46 to $48.33 a barrel on London's ICE Futures exchange.

The Greek elections caused some panic selling for West Texas Intermediate crude, which tested a new low within the first hour of this week's trading, but markets have somewhat calmed since then. WTI and Brent crude are expected to stay rangebound, analyst Daniel Ang at Phillip Futures said.

"This would likely go on until fundamentals change for the better," he said. He said currency markets could fluctuate more with the release of the U.S. Federal Reserve's latest meeting minutes later this week.

Nymex WTI crude lost 7.2% last week, settling at its lowest value since March 11, 2009. It has been down for 15 of the past 17 weeks, posting sharper losses than Brent crude, which lost around 2.8% last week.

Oil analysts are closely monitoring weekly drilling activity in the U.S. to get a sense of when the country's oil production will decline in response to low prices.

Houston energy investment banking Tudor, Pickering, Holt & Co. said a drop in the number of drilling rigs deployed in the U.S. would balance oil markets by the end of 2015 as a production slowdown becomes increasingly visible.

"A nearly 800-rig drop in our expected 2015 U.S. rig count drives a move from growth to a 2016 contraction in U.S. oil production," the bank said. It expects U.S. oil prices to rise from $50 a barrel in the first half of this year, to $90 a barrel by the end of 2016.

Morgan Stanley said shale-oil producers could be viable at an oil price as low as $30 and as high as $100, but lower prices should limit cash flow and spending, and restrict access to capital for oil producers.

"However, when prices rebound, US shale producers will be able to respond in 3-6 months," it said in its January energy outlook report.

Nymex reformulated gasoline blendstock for February--the benchmark gasoline contract--fell 146 points to $1.3333 a gallon, while February diesel traded at $1.6443, 24 points lower.

ICE gas oil for February changed hands at $473.00 a metric ton, down $4.00 from Friday's settlement.

Write to Eric Yep at eric.yep@wsj.com

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