Benchmark oil for August delivery was up 39 cents at $84.14 a barrel at late afternoon Singapore time in electronic trading on the New York Mercantile Exchange. The contract fell $1.21 to close at $83.75 in New York on Monday.
In London, Brent crude for August delivery was up 28 cents at $97.62 per barrel on the ICE Futures exchange.
Crude plunged to $77 last week from $106 two months ago on expectations slowing growth in the U.S., Europe and China would reduce oil consumption.
However, some analysts say investors have been too pessimistic about the global economy and, outside of Europe, crude demand has held up so far.
"While much of the severe sell-off in crude oil prices in May and June has been driven by fear of what could happen to world oil demand, we have not witnessed a collapse in demand yet," Goldman Sachs said in a report.
Traders are also closely watching the impact of tighter sanctions starting July 1 by the U.S. and Europe against Iran over the country's nuclear program. Iran, OPEC's second-biggest producer, is finding fewer countries willing to buy its crude, which could pinch global supplies.
"U.S. and E.U. sanctions against Iran are now in effect, and look to have a greater impact than we had anticipated," said Goldman Sachs, which forecasts oil will surge to $115 within three months. "The loss in Iranian exports could soon rival the loss of Libyan crude oil supplies last year."
In other energy trading, heating oil was up 1.5 cents at $2.69 per gallon while gasoline futures advanced 1.3 cents at $2.64 per gallon. Natural gas gained 1.6 cents at $2.84 per 1,000 cubic feet.