Brent crude futures were up 20 cents, or 0.3%, at $62.34 a barrel by 0644 GMT. U.S. West Texas Intermediate crude gained 20 cents, or 0.4%, to $54.10 a barrel.

Brent crude futures were trading 18 cents down at $60.76 a barrel by 1203 GMT. U.S. West Texas Intermediate crude futures lost 3 cents to $51.90.

OPEC and 10 non-OPEC partners, led by Russia, agreed in December to cut a combined 1.2 million b/d of production in the first half of 2019.

Brent futures fell 25 cents, or 0.4%, to $61.76 a barrel by 0750 GMT, having gained 1.1% on Friday. U.S. West Texas Intermediate (WTI) crude futures were down 22 cents, or 0.4%, at $52.29, having firmed by 0.4% in the previous session.

"Today about 18 million barrels of oil on a daily basis flows through this choke point coming from Saudi Arabia, emirates and other countries to China, Japan, India and other Asian customers." "But at the same time it is a major route for LNG, liquefied natural gas. About 30% of LNG goes through this strait, coming again to Japan, South Korea, and other Asian countries."

Brent crude futures were up 23 cents, or 0.4%, at $61.54 a barrel by 0638 GMT, having settled up 2.2% on Thursday. U.S. West Texas Intermediate crude futures were down 1 cent at $52.27 a barrel, after earlier rising. WTI also closed up 2.2% in the previous session, but is on course for a weekly decline of 3.2%.

Brent crude futures were up $1.91, or 3.18%, at $61.88 a barrel by 1039 GMT, having risen as much as 4.45% to $62.64. U.S. West Texas Intermediate crude futures were up $1.42, or 2.78%, at $52.56 a barrel. WTI earlier rose as much as 3.85% to $53.11.

In all, OPEC's 14 members pumped 30.09 million b/d in May, a 170,000 b/d fall from April and the lowest since February 2015, before Gabon, Equatorial Guinea and the Republic of Congo joined and Qatar was still a member,

Front-month Brent crude futures were at $62.56 at 0707 GMT, up 27 cents, or 0.4%, from Monday’s close. U.S. West Texas Intermediate (WTI) crude futures were at $53.75 per barrel, 49 cents, or 0.9%, above their last settlement.

Even so, OPEC said it would tread cautiously. The organization forecast that 2019 oil consumption will rise 1.14 million b/d year-on-year, a downward revision of 70,000 b/d from last month's report, as "significant downside risks from escalating trade disputes spilling over to global demand growth remain."

Front-month Brent crude futures were at $62.56 at 0707 GMT, up 27 cents, or 0.4%, from Monday’s close. U.S. West Texas Intermediate (WTI) crude futures were at $53.75 per barrel, 49 cents, or 0.9%, above their last settlement.

Brent crude futures were up $1.35 at $63.02 a barrel by 0757 GMT. WTI crude futures were up $1.10 at $53.69 per barrel.

U.S. exports of liquefied natural gas (LNG) to Europe have increased substantially since October 2018, averaging 1.9 billion cubic feet per day (Bcf/d) in the winter of 2018–19 compared with 0.1 Bcf/d in the winter of 2017–18.

Brent crude futures were at $60.50 at 0108 GMT. That was 13 cents, or 0.2%, below last session’s close. WTI crude futures were at $51.62 per barrel, 6 cents, or 0.1%, below their last settlement.

US crude oil inventories for the week ended May 31, excluding the Strategic Petroleum Reserve, increased by 6.8 million bbl from the previous week, according to data from the US Energy Information Administration.