Brent futures have jumped over 25 per cent since hitting an intraday low of $27.10 a barrel on January 20 and are heading for their fourth straight session of gains.
Brent had risen 38 cents to $34.27 a barrel by 0337 GMT, after ending up 79 cents, or 2.4 per cent, at $33.89 on Thursday.
US crude climbed 35 cents to $33.57 a barrel, having settled up 92 cents, or 2.9 per cent, at $33.22 on Thursday. US crude is also set for a 4.6 per cent weekly gain.
"Despite the unlikely scenario of supply cutbacks in the oil market, prices have found some support above $30 a barrel. We believe this basis is fragile, with fundamentals expected to weaken in the coming weeks," ANZ said on Friday.
"The likelihood of an agreement between producers is extremely low. In the absence of a supply cut, there is further downside risk to prices in the short term."
Brent futures rallied as much as 8 per cent after Russia said on Thursday that OPEC's largest producer Saudi Arabia had proposed oil production cuts of up to 5 per cent in what would be the first global deal in over a decade to help clear a glut of crude and prop up sinking prices.
"We remain highly sceptical that such a meeting will result in credible cuts in supply; thus, we see this as nothing more than an attempt to shift market sentiment, and we do not expect that it will change the physical market imbalance," Barclays said Thursday, referring to meetings between OPEC members and Russia.
"The price path implied by our forecasts, of Brent trading less than $40 a barrel for at least two quarters, is required for the balancing process to take place, paving the way for a more sustainable increase in prices."
London-based capital market analysts Edison Investment Research has reduced its 2016 oil price forecast to $40 a barrel from $60.
"The oil markets have been in turmoil now for 16 months, with January 2016 trading the most tumultuous we have seen in years," said Edison analyst Ian McLelland.
Oil volatility has climbed to its highest since 2009 as traders try to price in the uncertainty around supply cuts. At-the-money implied volatility for both WTI and Brent has surged this week. Implied volatility is a measure of expectations for future market price turbulence.
Outright close-to-close price volatility is also at 2008/2009 levels.