Brent futures rose $4, or 4 percent, to $103.94 a barrel at 0400 GMT, while US West Texas Intermediate (WTI) climbed $3.49, or 4 percent, to $91.62.
Crude futures had dropped more than 10 percent on Monday after Trump ordered a five-day delay to planned attacks on Iran's power plants, claiming that the US had held talks with unnamed Iranian officials that yielded "major points of agreement".
"By shelving the plan to strike Iranian power plants for five days, the US effectively sucked much of the 'war premium' from the oil price," said KCM Trade chief market analyst Tim Waterer.
"Today's moderate bounce is just the market finding its footing in the mud. Traders are aware that while the missiles are on hold, the Strait of Hormuz is still far from a clear waterway."
The war has all but halted shipments of about one-fifth of the world's oil and liquefied natural gas through the Strait of Hormuz.
However, two tankers bound for India sailed through the strait on Monday.
Tehran rejected the claim of contact with Washington, dismissing it as an attempt to manipulate financial markets, while Iran's military said they had attacked US targets and denounced Trump's comments as "worn-out psychological operations".
"Even with a possible decrease in tensions after (Monday's) announcement from President Trump, we expect a price floor of $85–$90 and a natural drift back to the $110 range until the Strait of Hormuz is restored," Macquarie said in a client note.
If the strait remains effectively shut until the end of April, Brent could still reach $150 a barrel, Macquarie said.
In the latest attacks on energy infrastructure across the region, a gas company office and a pressure-reduction station were hit in the Iranian city of Isfahan, while a projectile struck a gas pipeline feeding a power station in Khorramshahr.
To ease supply shortage, the US temporarily waived sanctions on Russian and Iranian oil already at sea.
Industry sources said traders have since offered Iranian crude to Indian refiners at a premium to ICE Brent.
The International Energy Agency Executive Director Fatih Birol on Monday said the agency is consulting Asian and European governments on possible further releases of strategic reserves "if necessary".
Still, markets are bracing for market disruption at least until April, which continues to be a tailwind beneath Brent while maintaining momentum for inflation, said Priyanka Sachdeva, senior market analyst at brokerage Phillip Nova.
Oil executives and energy ministers at a conference in Houston flagged the longer-term impact of the US–Israel war with Iran on the global economy. Meanwhile, the US Energy Secretary Chris Wright downplayed the crisis.