Companies including BP, Chevron and Equinor ASA evacuated rigs, and so far producers have shut 16%, or 293,656 barrels per day (bpd) of oil output due to Hurricane Zeta.
Brent crude was up 14 cents, or 0.3%, at $45.10, heading for a gain of about 1.6% this week
West Texas Intermediate crude futures rose 50 cents, or 1.2%, to $41.72 a barrel at 0301 GMT, while Brent crude futures were up 40 cents, or 0.9%, at $44.80 a barrel
Oil also drew support from signs that talks between the White House and Democrats in Congress on a new coronavirus relief package are making progress, although the sides remain far apart
Brent crude futures were up 10 cents, or 0.2%, at $43 a barrel as of 0049 GMT, and US West Texas Intermediate (WTI) crudefutures rose 14 cents, or 0.4%, to $40.43 a barrel
The lifting of some coronavirus curbs is driving a recovery in gasoline demand with traffic congestion in some of the world's capitals returning to year-earlier levels
Prices have risen in the past two weeks as some countries relaxed coronavirus restrictions and lockdowns, giving hope for a pickup in fuel demand
US West Texas Intermediate (WTI) crude futures were up 1 per cent, or 24 cents, at $24.38 after touching a high of $24.77
Together with Rs 39,000 crore in annual revenues gained from the March 14 excise duty hike of Rs 3 per litre each on petrol and diesel, the government stands to gain as much as Rs 2 trillion
OANDA's Moya cautioned that the selling could start again in oil markets.
Brent crude futures rose 74 cents, or 1.2%, to $62.87 a barrel by 12:56 pm EST (1756 GMT). US West Texas Intermediate crude futures rose 68 cents, or 1.2%, to $57.22 a barrel
On Friday, prices jumped by about $2 a barrel after U.S. officials said a deal could be signed this month.
Brent crude futures LCOc1 gained $1.31, or 2.2%, to $60.41 a barrel by 11:27 a.m. EDT (1527 GMT), after earlier reaching a session high of $60.65 a barrel
International benchmark Brent crude futures, were at $57.61 a barrel by 0009 GMT, up 23 cents, or 0.4%, from their previous settlement
Prices edged higher by about 0.6% on Wednesday after a report showed a contraction in U.S. crude stockpiles
Brent crude oil futures were at $67.82 per barrel at 0122 GMT, down 4 cents from their last close but within a dollar of the $68.69 per barrel 2019-high marked the day before
Opec, as well as some non-affiliated producers like Russia, agreed late last year to cut output by 1.2 million barrels per day to prevent a large supply overhang from swelling more
Brent has risen nearly 12% so far in Jan, which would be the largest monthly percentage increase since Dec 2016
International Brent crude oil futures were at $59.64 per barrel, up 65 cents, or 1.1%, from their last close
Brent crude futures rose $2.23 to settle at $61.69 a barrel, a 3.75 percent gain