Gasoline and diesel prices are displayed at a gas station in Vernon Hills, Ill., Friday, April 1, 2022. (AP Photo)
European Union officials were discussing new measures against Moscow after reports -- denied by the Kremlin -- that troops had executed civilians.
Among the punishments could be a ban on imports of Russian crude, following a similar move by the United States and Britain.
White House National Security Advisor Jake Sullivan also signalled more US sanctions were on the way this week.
While Europe's economy -- particularly Germany's -- relies heavily on energy from Russia, the possibility of an embargo sent both main contracts sharply higher Monday, and they continued their rise in Asia, putting on more than one percent.
That pared some of the sharp losses seen Friday in reaction to a pledge by Washington and other major economies to unleash millions of barrels from their stockpiles to keep a lid on prices, which are fanning already high inflation.
It also offset an expected hit to demand in China from lockdowns in parts of the country -- including Shanghai, the biggest city -- sparked by a wave of Omicron outbreaks.
"In the wake of 'Russian atrocities' claims and the ensuing public outrage, there is a strong chance we could see another layer of sanctions on Russian energy," said SPI Asset Management's Stephen Innes.
"The receptiveness on the part of Europe (including Germany) to refrain from importing Russian gas has put a bid under and should keep energy prices supported."
The continued uncertainty caused by the war in Ukraine, and the blow to the global economy it is expected to deal, was unable to prevent another healthy performance on Wall Street, where the Nasdaq's surge led all three main indexes higher.
"Despite all the concerns, equities remain the best bet to achieve returns above today's elevated inflation," said markets strategist Louis Navellier.
Trade was tepid in Asia, with Hong Kong, Shanghai and Taipei closed for holidays but most markets rose.
Tokyo, Sydney, Seoul, Singapore, Jakarta, Bangkok and Wellington were slightly up, though Mumbai and Manila dropped.
London, Paris and Frankfurt all opened on the front foot.
Traders will be keeping a close eye on the release this week of minutes from the Federal Reserve's most recent policy meeting, hoping for an insight into officials' thinking over monetary policy.
After last month's expected 0.25 percentage point interest rate hike, there are increasing bets on a half-point lift in May in light of soaring inflation and strong jobs data that suggest the economy remains robust enough to absorb higher borrowing costs.
And National Australia Bank's Tapas Strickland added: "Profit reporting season in the US kicks off next week and it will be interesting to see how firms are interpreting the tea leaves, and whether earnings guidance is revised down."