Ongoing anticipation over the return of Iranian oil, and emerging stability in the U.S. oil sector, pushed crude oil prices slightly lower in Monday trading.

Brent crude oil prices fell nearly a full percentage point to $56.59 per barrel early in the Monday trading day. West Texas Intermediate, the U.S. benchmark, did better, losing less than half a percent to $50.89 per barrel.

Crude oil prices are flirting with 2015 lows amid ongoing concerns about the health of the global economy in an era of surplus supplies. Greek debt issues re-emerged as a short-term threat to the Eurozone after a default to the International Monetary Fund.

Greek banks reopened Monday, but only to limited cash withdrawals.

On the supply side, oil services company Baker Hughes in its latest report showed a modest decline in the number of rigs deployed in North American basins. The slump in crude oil prices means less available capital for exploration and production, though rig numbers paint a mixed picture about the health of the sector.

North Dakota's rig count of 73 was unchanged from the previous week. State government data show oil production for May, the last full month for which data are available, was 1.2 million barrels per day, just shy of the all-time high of 1.22 million bpd posted in December.

The U.N. Security Council, meanwhile, voted unanimously in favor of last week's deal that restricts Iran's nuclear program in return for staged sanctions relief. Under the existing sanctions regime, Iranian crude oil exports are limited to around 1 million bpd, about half of its full potential.