Equities rallied Tuesday as investors cheered a further easing of lockdowns in some countries, which offset fears of a renewed trade war between China and the United States.
Oil also rose as the economic outlook seemed to brighten with the markets' peak-to-trough fall now less than half what it was earlier in the crisis.
With signs that the spread of coronavirus is easing, governments in Europe and parts of Asia-Pacific as well as some US states have begun to allow businesses to reopen.
"Markets have reacted to the fact that it seems that there is a little light at the end of the tunnel," Scope Markets analyst James Hughes told AFP.
"Lockdown easing in the likes of Spain and Italy has led to many looking at timelines for many aspects of life reopening," he said.
Fawad Razaqzada, market analyst with ThinkMarkets, cautioned that while a gradual return to economic activity would bring optimism, the long-term view was still grim.
"Incoming macro data continue to reveal that the damage from COVID-19 is worse than expected, reducing the likelihood we will see a V-shaped economic recovery when the lockdown measures are mostly lifted," Razaqzada said.
Markets took an optimistic view with Frankfurt closing up 2.5 percent and London ending not far behind. On Wall Street, the Dow Jones index had added 1.7 percent some two hours into the session.
With oil posting double-digit percentage gains, British energy giant BP rose six percent in its slipstream to 318.90 pence while Royal Dutch Shell B shares added 5.06 percent to close at 1,283.40 pence.
- 'On the right path' -
"Even if the full return to normal life is not yet on the cards, the recent moves at least give many the sense that we are on the right path," Hughes said.
The gains helped markets claw back some of Monday's steep losses, though there remains a sense of fear of a second wave of infections, as traders also contemplate a long recovery from the economic destruction.
Hong Kong closed higher on news that some restrictions would be lifted in the city, outweighing data showing its economy suffered its worst contraction on record in the first quarter.
Dealers were keeping tabs on China-US relations after Donald Trump hit out at Beijing over its handling of the outbreak, saying it began in a Wuhan lab, but so far offering no evidence.
The comments, and his warning he could hit China with fresh tariffs, have fanned fears of a repeat of the standoff between the economic superpowers that battered markets last year.
In forex exchange markets the euro slipped against the dollar after Germany's top court cast doubt on the legality of the European Central Bank's massive bond buying programme.
- Key figures around 1545 GMT -
London - FTSE 100: UP 1.7 percent at 5,849.42 points (close)
Frankfurt - DAX 30: UP 2.5 percent at 10,729.46 (close)
Paris - CAC 40: UP 2.4 percent at 4,483.13 (close)
EURO STOXX 50: UP 2.0 percent at 2,872.75
New York - Dow: UP 1.6 percent at 24,139.40
Hong Kong - Hang Seng: UP 1.1 percent at 23,868.66 (close)
Shanghai - Composite: Closed for a holiday
Tokyo - Nikkei 225: Closed for a holiday
Brent North Sea crude: UP 10.5 percent at $30.05 per barrel
West Texas Intermediate: UP 16.6 percent at $23.78
Euro/dollar: DOWN at $1.0840 from $1.0907 at 2100 GMT
Dollar/yen: DOWN at 106.56 yen from 106.74
Pound/dollar: UP at $1.2453 from $1.2443
Euro/pound: DOWN at 87.09 pence from 87.66 pence