Brent crude futures rose 38 cents, or 0.61%, to $62.53 a barrel at 0507 GMT, after falling 4.2% on Monday.
U.S. West Texas Intermediate (WTI) crude futures rose 34 cents, or 0.58%, to $58.99 barrel, after sliding 4.6% on Monday.
Market sentiment was buoyed by a survey from the Institute for Supply Management (ISM) on Monday showing activity in the U.S. services industry reached its highest level on record in March. The data came after a jobs report on Friday beat forecasts with 916,000 added to the U.S. economy last month.
The U.S. data “underscored growth momentum in the world’s largest economy, brightening the energy demand outlook,” said DailyFX strategist Margaret Yang.
Adding to positive sentiment, a recovery in China’s services sector picked up speed in March as firms hired more workers and business optimism surged, a private sector survey showed on Tuesday.
In addition, England is set to ease coronavirus pandemic restrictions on April 12, with the opening of businesses including all shops, gyms, hair salons and outdoor hospitality areas.
Those helped offset worries about the agreement last week by the Organization of the Petroleum Exporting Countries (OPEC) and allies, known as OPEC+, to bring back 350,000 barrels per day (bpd) of supply in May, another 350,000 bpd in June and a further 400,000 bpd or so in July.
Saudi Arabia is also set to phase out its extra voluntary cut of 1 million bpd over those three months. At the same time OPEC member Iran, exempt from making voluntary cuts, is boosting supply.