U.S. crude settled down 3 cents to $61.67 a barrel, still close to its highest levels since January 2020. Brent crude settled up 13 cents, or 0.2%, to $65.37 a barrel.

Both contracts rose more than $1 earlier before retreating.

Shale oil producers and refiners in the southern United States are slowly resuming production after 2 million barrels per day (bpd) of crude output and nearly 20% of U.S. refining capacity shut down because of last week's winter storm.

Traffic at the Houston ship channel was slowly returning to normal. Production, however, was not expected to fully restart soon and some shale producers forecast lower oil output in the first quarter.

Some oil production may never come back, commodities merchant Trafigura said on Tuesday.

After the cold snap, U.S. crude oil stockpiles were also seen falling for a fifth straight week, while the inventories of refined products also declined last week, an extended Reuters poll showed. [EIA/S]

"It appears that last week's severe cold spell and related Texas power outage could be affecting the weekly EIA data into the middle of next month," said Jim Ritterbusch, president of Ritterbusch and Associates in Galena, Illinois.

There were also concerns over the U.S. economic recovery, which the chair of the Federal Reserve, Jerome Powell, said remained "uneven and far from complete."

He said it would be "some time" before the central bank considered changing policies it had adopted to help the country back to full employment.

Commerzbank analyst Eugen Weinberg said the recent oil price rise was buoyed by upbeat price forecasts from U.S. brokers.

Goldman Sachs expects Brent prices to reach $70 per barrel in the second quarter from the $60 it predicted previously, and $75 in the third quarter from $65 forecast earlier.

Morgan Stanley, which expects Brent to reach $70 in the third quarter, said new COVID-19 cases were falling while "mobility statistics are bottoming out and are starting to improve".

Bank of America said Brent prices could temporarily spike to $70 in the second quarter.

(Reporting by Laura Sanicola in New York; Additional reporting by Bozorgmehr Sharafedin in London and Jessica Jaganathan in Singapore; Editing by Matthew Lewis and Mark Heinrich)

By Laura Sanicola