LONDON: Oil prices fell on Monday as worries about oversupply in North America and a strong dollar pushed Brent futures towards $ 59 a barrel and US contracts below $ 49 a barrel.

After an initial rise along with global markets on optimism that another euro zone crisis over Greek debt had been averted for now, prices began dipping as analysts said crude markets remained oversupplied, especially in the United States.

“The term structure of oil continues to weaken and inventories keep piling up,” Bank of America Merrill Lynch said in a note. Brent crude was trading $ 1 lower at $ 59.34 at 1123 GMT. Benchmark US WTI crude April futures were trading down 63 cents at $ 49.71 a barrel.

WTI’s March futures settled at $ 50.34 a barrel on Friday, expiring as the front-month contract.

The dollar was up 0.6 percent against a basket of currencies , making dollar-traded commodities such as oil more expensive for those holding other currencies.

“The USD index has been trading near 94.85 eyeing the key 95.0 level, adding pressure to the oil market,” said Myrto Sokou, senior research analyst at Sucden Financial, in a note. Oil prices more than halved between June and January, with Brent front-month futures reaching a low of $ 45.19 a barrel on Jan. 13.

Since then, prices have picked up. Brent futures jumped to $ 63 a barrel last week as traders closed longstanding short positions in reaction to a falling US rig count.

Morgan Stanley warned that US crude stocks – currently at record highs – were set to build through May.

“Despite optimism about the large drop in the US rig count in recent weeks, the pace of decline has been decelerating,” it said.

“A further slowing would only reinforce concerns that a large production decline could take longer.” US drilling has slowed this year as producers react to the collapse in oil prices, but Goldman Sachs also said the pace of the US rig count decline was now slowing.

US oil production growth is expected to reach 440,000 barrels per day by the fourth quarter of 2015 compared with a year before, based on the current rig count, Goldman said in a note.

Analysts said a US cold spell could also prevent crude prices from rising further. US East Coast refineries have been hit by cold weather, sending up heating oil futures on fears of tight supplies.