Oil prices climbed again on Tuesday after a jump in the morning session, holding near a 13-month high, due to the slow return of U.S. crude output impacted by freezing winter conditions in Texas that forced the shutdown of crude production last week.

Shale oil producers in the southern United States are expected to need at least a fortnight to fully restart the more than 2 million barrels per day (bpd) of crude output that shut down in the wake of frigid weather conditions that resulted in pipes freezing and power supply disruptions slackening their recovery, according to sources.

International benchmark Brent crude futures increased by 28 cents, or 0.4%, to hit $65.52 per barrel by 01:02 GMT, while U.S. crude oil gained 14 cents, or 0.2%, to reach $61.84 a barrel. Both benchmarks increased almost 4% in the earlier session.

"The positive momentum continues in the oil complex, with investors unabashedly predisposed to a bullish view," Stephen Innes, chief global markets strategist at Axi, stated in a note.

"Several significant oil price revisions were announced overnight and may have contributed to the rally of over 3%," Innes pointed out.

Goldman Sachs Commodities Research increased its Brent crude oil price projections by $10 for the second and third quarters of 2021, quoting lower expected inventories and steeper marginal costs to restart upstream activity and speculative inflows.

The Wall Street bank projects Brent prices to reach $70 per barrel in the second quarter, from its earlier forecasted $60 and $75 in the third quarter, and from an earlier $65.

Morgan Stanley forecasts Brent at $70 per barrel in the third quarter, in view of the "signs of a much improved market," including predictions of improvement in demand.

Moreover, supporting prices, OPEC, and U.S. oil companies expect a subdued rebound in the shale oil supply this year, as top U.S. producers freeze output, in spite of a spike in prices, which is a decision that would work in favor of OPEC and its allies.

A preliminary Reuters poll on Monday attributed the decline in stockpiles of U.S. crude oil and refined products to the disruption in Texas.