With Iran downplaying Israel's reported attack on the country, which came days after a drone and missile strike by Tehran, tensions between the regional rivals cooled.
While the situation remains tense, the lack of escalation over the weekend provided traders with an opportunity to pick up equities and helped push oil down.
The gains came despite a largely negative lead from Wall Street, where the Nasdaq shed more than two percent owing to hefty selling in tech giants including Amazon, Apple and Netflix.
Investors are now setting their sights on the personal consumption expenditures (PCE) index, the Federal Reserve's preferred gauge of inflation, which is due Friday.
The reading could play a major role in the central bank's decision-making on interest rates and comes after a third successive month of above-forecast consumer price index figures.
The disappointing CPI data has dented hopes for a cut in June, while traders have scaled back their outlook for how many the Fed will make this year.
The PCE report is followed by the bank's policy announcement next week, which will be pored over for clues about its next step.
Several officials have lined up to temper expectations for cuts, citing sticky inflation as well as a still-strong economy and labour market.
Chicago Fed boss Austan Goolsbee said last week that the battle against surging prices had stalled.
"Right now, it makes sense to wait and get more clarity before moving," he said, warning that bringing inflation back to the bank's two percent goal would likely take longer than initially thought.
Earnings from big-name firms including Google parent Alphabet, Tesla and Microsoft are also in play this week, with investors hoping for strong reports to back up a recent surge in equities.
- Key figures around 0230 GMT -
Tokyo - Nikkei 225: UP 0.7 percent at 37,334.97 (break)
Hong Kong - Hang Seng Index: UP 2.5 percent at 16,625.93
Shanghai - Composite: UP 0.2 percent at 3,072.00
Dollar/yen: UP at 154.68 at 154.64 yen on Friday
Euro/dollar: UP at $1.0667 from $1.0658
Pound/dollar: UP at $1.2388 from $1.2373
Euro/pound: UP at 86.13 pence from 86.11 pence
West Texas Intermediate: DOWN 0.8 percent at $81.58 per barrel
Brent North Sea Crude: DOWN 0.8 percent at $86.62 per barrel
New York - Dow: UP 0.6 percent at 37,986.40 (close)
London - FTSE 100: UP 0.2 percent at 7,895.85 (close)
dan/mtp
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