Crude futures rose on Monday after gaining over 15% last week, with some indicators pointing to the possibility the market could be bottoming out.
Brent futures had climbed almost half a dollar, or 1.2%, from their previous close to $35.51 a barrel early on Monday.
US West Texas Intermediate crude futures were up 16 cents at $32.94 a barrel after gaining over 15% the previous week.
Analysts said that first signs of a stronger outlook were appearing after a 20-month rout that has seen prices fall by 70%.
"The US crude market seems to have passed the worst point and crude runs should start creeping higher, taking pressure off inventory levels," said Richard Gorry, director of JBC Energy Asia.
"The latest EIA data on US production is also supportive as it indicates that the low prices are finally having an impact," he said, referring to numbers from the US Energy Information Administration.
US shale producers cut oil rigs for a 10th week in a row to the lowest levels since December 2009, data showed on Friday, which analysts expect will lead to a production fall of 600,000 barrels per day this year.
Morgan Stanley said a potential Russian/Saudi agreement to freeze output at January levels could also drive prices.
"Russia said production freeze agreement discussions should end on March 1... Any news of progression could drive headlines and prices," the bank said, but added that "we still question the efficacy of a freeze."
Market data also suggests early signs of shifting sentiment.
The amount of open positions in WTI crude contracts that bet on a further fall in prices has fallen over 17% since mid-February to their lowest level in 2016, although by historic levels their amount remains high.
At the same time, financial speculators have sharply raised their bullish bets on oil after talk of a global production freeze and signs of falling US shale crude output and growing gasoline demand.
Money managers raised their combined net long position in crude futures and options in New York and London by nearly 16% for the week ended 23 February, data by the US Commodity Futures Trading Commission (CFTC) showed.
ING bank said that technical market indicators "could be the early warning sign of a coming trend change."
Despite this, JBC's Gorry said there was also "still a lot of downside risk" due to the huge overhang in production and stored supplies, which in the United States are at historic highs.