Brent crude futures gained 81 cents, or about 1.04%, to $78.96 a barrel at 1333 GMT. The contract had lost 14 cents on Monday.
U.S.
West Texas Intermediate crude was up 41 cents, or 0.56%, from Friday at $73.09 a barrel. U.S.
markets were closed for a public holiday on Monday.
An escalating conflict in the Middle East, and consequently increased volatility in oil futures, focused attention on Tuesday.
«The brief spikes we've seen have highlighted the sensitivity in the market to events around the Red Sea,» said Craig Erlam of OANDA.
Yemen's Houthi movement said on Monday it will expand its targets in the Red Sea region to include U.S. ships, and that it would keep up attacks after U.S.-led strikes in Yemen.
A Malta-flagged bulk carrier was struck by a missile off Yemen on Tuesday.
More oil tankers have sought to avoid the southern Red Sea.
Japan's largest shipper by sales NYK told Reuters it has instructed all vessels it operates not to use the Red Sea.
Oil major Shell said it had suspended all shipments through the Red Sea indefinitely after last week's strikes, the Wall Street Journal reported.
Tensions are flaring elsewhere in the region. Iran said on Tuesday it had launched ballistic missiles at targets in Iraq and Syria in defence of its sovereignty and to counter terrorism.
The geopolitical risk premium on oil prices may find a ceiling unless production is shut in, analysts said.
«In the absence of actual and palpable impact on oil output prices will remain well within the current $72-$82 range,» PVM analyst Tamas Varga said in a note.
Investors were also awaiting a speech by the U.S.