Brent, the benchmark for two thirds of the world’s oil, was up 0.2 per cent at $78.24 a barrel on Tuesday at 3.05pm UAE time. West Texas Intermediate, the gauge that tracks US crude, was trading 0.21 per cent higher at $72.96 a barrel.
Brent rallied 4.2 per cent on Monday to settle at $78.12, while WTI surged 5.1 per cent to $72.81.
"Oil prices are continuing to recover after popping higher at the start of the week," Craig Erlam, senior market analyst at Oanda, said.
"There's been a broad improvement in risk appetite at the start of the week thanks to a weekend without drama in the banks. That's enabled stocks to bounce back and yields to creep higher on stronger economic prospects which, in turn, is lifting crude prices."
The rally on Monday was also supported by a halt to exports from Iraq's Kurdistan region which knocked around 450,000 barrels per day offline, he said.
A legal dispute between Iraq, its semi-autonomous Kurdistan region and Turkey has halted the supply of crude exports to the global market this week.
Iraq won a long-standing arbitration case against Turkey that led to the halting of crude exports from Turkey’s Ceyhan port, which added to supply concerns in an already tight market.
"There's no timeline for an agreement to be reached to restart flows and the tighter the oil market becomes, the greater the loss it will be. For now, it's contributed to a small rise in the price, with Brent now trading around the lows of the months that preceded the ... banking crisis," Mr Erlam said.
The collapse of US lender Silicon Valley Bank earlier this month triggered a turbulent period that stoked fears of a global banking crisis similar to when Washington Mutual collapsed in 2008.
In the days after SVB's collapse, mid-size lenders Signature and Silvergate Bank both failed and shares tumbled at other regional banks.
Contagion fears also spread to Europe, where Switzerland's Credit Suisse was acquired by rival UBS in a deal engineered by Swiss government authorities.
On Monday, however, the Federal Deposit Insurance Corporation confirmed that US lender First Citizens Bank & Trust will acquire the troubled SVB.
Oil prices are also likely to draw strength in the short term from indications of a continued recovery of crude demand in China.
China's oil imports are expected to rise 6.2 per cent in 2023 to 540 million tonnes, Reuters said, citing a report by a research unit of China National Petroleum Corporation on Monday.
“In energy, improved sentiment in banks and a legal dispute that halted around 400,000 barrels a day of oil exports from the Ceyhan port in Turkey pushed US crude past the $70 per barrel yesterday. The price of a barrel flirted with the $73 level,” said Ipek Ozkardeskaya, senior analyst at Swissquote Bank.
“Yet, the mounting recession odds and the resilient Russian supply, which partly absorbs the rising oil demand from China, are expected to keep the topside limited into the $75 to $77 area.”