Brent crude futures gained $2.51, or 7.3 percent, to reach $36.87 per barrel on Tuesday, while US West Texas Intermediate (WTI) crude rose $2.15, or 6.9 percent, to $33.28 a barrel.
This comes after US President Donald Trump announced new economic stimuli on Monday, including payroll tax cuts and loans to small businesses.
Earlier, US stocks lost more than 7 percent of their value on Monday, with the Dow Jones Industrial Average index alone falling more than 2,000 points - its worst one-day decline since 2008 - after a historic oil price crash and panic selling across markets induced by fears over the novel coronavirus (COVID-19) outbreak.
Stock markets across the world tumbled on Monday, amid fears over the coronavirus disease, and the fall in global oil prices after the OPEC+ deal collapsed.
The Saudi-led Organisation of the Petroleum Exporting Countries (OPEC), failed to agree on deeper production cuts to mitigate demand lost to the coronavirus crisis.
OPEC has had production cutting pacts since 2016 with non-member allies led by Russia. The wider alliance, known as OPEC+, met in Vienna on Friday to discuss production cuts. After the talks, OPEC+ issued a statement saying it would continue consultations to stabilise the oil market, without mentioning any deeper cuts.