Oil prices surged on demand optimism ahead of the latest OPEC meeting on Tuesday, while the pound hit a three-year high against the dollar over Britain's economic rebound and equities mostly rose with focus on upcoming US jobs data.
Wall Street and London were closed Monday for holidays meaning there were few drivers for buying, with the general theme continuing to be the global economic recovery playing against fears about inflation and a possible taper of central bank monetary policy.
The rollout of vaccines around the world has allowed leaders of key economies including the United States and Europe to wind back the containment measures that sparked a recession last year.
That, combined with mind-boggling government spending splurges and central bank largesse, has been crucial to a rally in global equities from their March 2020 lows to record or multi-year highs.
Analysts expect more gains but warn the road will be bumpy as inflation spikes -- caused by a strong recovery in activity, supply issues, bottlenecks and a low base of on-year comparison -- lead to concern over possible central bank tightening.
The release of figures showing how many jobs were created in the United States last month is being keenly awaited for an idea about the strength of the recovery, with hopes for a sizeable jump after a disappointing miss in April.
After a tepid start to the day, Asian markets were broadly positive in the afternoon.
Hong Kong jumped more than one percent along with Wellington and Taipei, while Shanghai, Singapore, Seoul and Bangkok were all up, though there were small losses in Tokyo and Sydney, while Manila was flat.
Mumbai was also barely moved after data showed India's economy suffered its worst contraction since independence more than seven decades ago.
Kuala Lumpur saw little major reaction as Malaysia imposed a tough lockdown across the country to battle a new virus surge.
London returned from a long weekend to enjoy gains soon after the open, while Paris and Frankfurt were also up.
Oil prices powered higher ahead of the latest monthly gathering of OPEC and allies, with expectations that they will begin to lift output from next month as they grow confident that the world economy is well on the recovery track and demand will continue to improve.
The gains were also helped by comments from the group that it sees supplies tumbling this year as people slowly get back to some semblance of normality, while analysts said the possible return of Iranian crude to markets -- if it agrees a nuclear deal with world powers -- would not likely have a major impact.
"There's some confidence right now improving demand should be able to absorb what could be an additional two million barrels a day from Iran, if it materialises," said Howie Lee of Oversea-Chinese Banking Corp.
"Demand from the US has been driving the global consumption recovery."
Brent jumped back above $70 a barrel and WTI hit $68.26, its highest in two and a half years.
On currency markets, the pound was sitting around a more than three-year high as Britain's vaccine rollout continues and the country announced just one coronavirus-related death Monday, the lowest since the pandemic began.
The nation's healthy economic rebound is also leading to bets the Bank of England will be forced to tighten monetary policy sooner than expected and there are forecasts for the unit to break $1.45 for the first time since before the vote to leave the European Union in 2016.
China's yuan was slightly higher, though the country's central bank on Monday looked to rein in a recent rally by telling lenders they will have to increase their holdings of foreign reserves for the first time in 14 years, as it tries to quell speculation.
Tokyo - Nikkei 225: DOWN 0.2 percent at 28,813.34 (close)
Hong Kong - Hang Seng Index: UP 1.1 percent at 29,468.00 (close)
Shanghai - Composite: UP 0.3 percent at 3,624.71 (close)
London - FTSE 100: UP 0.9 percent at 7,088.44
West Texas Intermediate: UP 2.9 percent at $68.26 per barrel
Brent North Sea crude: UP 2.2 percent at $70.81 per barrel
Pound/dollar: UP at $1.4232 from $1.4207 at 1645 GMT
Dollar/yen: DOWN at 109.46 yen from 109.46 yen
Euro/dollar: UP at $1.2240 from $1.2227
Euro/pound: DOWN at 86.00 pence from 86.06 pence
New York - Closed for a holiday
-- Bloomberg News contributed to this story --