Front-month Brent crude futures were trading at $39.42 per barrel at 0620 GMT, up 1.8% from their last settlement and over a third higher than their January low, when prices fell to levels not seen since 2003.
U.S. West Texas Intermediate (WTI) futures were trading at $36.59 a barrel, up 67 cents from the last close and 40% above February lows.
"It looks at this stage as if it (oil) has formed a little bit of a bottom and perhaps we're going to see a sustained price in the $30s, maybe trending back up to $40 dollars at some point," said Ben Le Brun, market analyst at OptionsXpress.
"The macro picture takes all corners of the globe into account, and those corners seem to be improving and that's where I'm seeing the oil price tick higher."
Analysts said that strong US payroll data had pushed markets on Friday and early Monday, but that attention was now shifting to China where the National People's Congress opens its annual session this week.
On the supply side, US energy firms cut oil rigs for an 11th week in a row to the lowest level since December 2009, data showed on Friday, as producers slash costs.
Drillers removed eight oil rigs in the week ended March 4, bringing the total count down to 392, oil services company Baker Hughes Inc said.
Beyond a tightening supply outlook, traders said that shifting sentiment was also lifting prices as large amounts of short positions were being closed and bets rising prices opened.
Ric Spooner, chief market analyst at CMC Markets said "there's a good prospect that Brent could hit $40 (it) could easily do it in the next trading session."
Despite the recent price rises and the generally more bullish outlook, analysts warned that the general glut remained in place and prices could still drop back.
"Upside should be limited by bloated global inventories and producer hedging. Moreover, we worry that this latest oil bounce shares many features of the 2Q15 false oil rally," Morgan Stanley said on Monday.
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