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Asia kicked off the firmer trend, followed by London, Frankfurt and Paris which all closed higher on burgeoning investor optimism after yet another record finish on Wall Street ahead of the weekend.
Approaching midday in New York on Monday, American stocks were poised for further gains.
"US stocks are higher in early action, with geopolitical concerns continuing to fade and the global markets shrugging off heightened monetary policy uncertainty ahead of this week's decisions by the Fed and Bank of Japan, on the heels of hawkish signals by the Bank of England and European Central Bank," analysts at the Charles Schwab brokerage told clients.
Fading North Korea tensions have persuaded many investors to remove their cash from haven investments like gold and plough it back into riskier equities.
Fears over North Korea receded soon after Friday's second missile test in a month. While the launch over Japan revived geopolitical worries - especially as it came soon after Pyongyang's provocative nuclear test - analysts said investors were calm for now.
"European stocks market are in positive territory today as geopolitical tensions cool," said David Madden, market analyst at trading company CMC Markets UK.
'HAPPY TO BUY'
"The standoff in relation to North Korea is still ongoing, but seeing as there has been no fresh negative developments, dealers are happy to buy into stocks," he added.
Investor focus is now turning towards this week's US Federal Reserve monetary policy meeting, which ends on Wednesday.
Markets will be closely watching the US central bank as its policymakers deal with the fallout from Hurricanes Harvey and Irma, which hammered the country and are expected to hit economic growth.
While the Fed is tipped to keep borrowing costs on hold, the bank's plans for cutting back crisis-era bond-buying stimulus and any signals about the future of interest rates will be pored over.
But analysts were unsure about any further increases this year with inflation remaining subdued - apart from a bigger-than-expected jump in August - and other indicators still soft.
Despite the trend towards monetary tightening, stock markets remain buoyant and on Friday the Dow and S&P 500 both closed at all-time highs.
POUND KICKS ON
The pound meanwhile continued to shine against the dollar after the Bank of England indicated last week that it would probably tighten monetary policy itself very soon.
BoE governor Mark Carney said on Thursday that the chances of a rise had increased. This was followed on Friday by another policymaker signalling a move in the coming months.
Central banks are shifting from their easy-money policies as the world economy slowly improves, and the European Central Bank is also set to wind down its own stimulus.
The pound declined on Monday, ducking underneath US$1.36, but remained close to its highest level against the dollar since Britain voted to leave the European Union in June 2016.
Key figures around 1535 GMT:
London - FTSE 100: UP 0.5 per cent at 7,253.28 points (close)
Frankfurt - DAX 30: UP 0.3 per cent at 12,559.39 (close)
Paris - CAC 40: UP 0.3 per cent at 5,229.32 (close)
EURO STOXX 50: UP 0.3 per cent at 3,526.74
New York - DOW: UP 0.4 per cent at 22,351.62
Hong Kong - Hang Seng: UP 1.3 per cent at 28,159.77 (close)
Shanghai - Composite: UP 0.3 per cent at 3,362.86 (close)
Tokyo - Nikkei 225: Closed for public holiday
Euro/dollar: UP at US$1.1951 from US$1.1947 at 2100 GMT
Dollar/yen: UP at 111.54 yen from 110.86 yen
Pound/dollar: DOWN at US$1.3524 from US$1.3593
Oil - Brent North Sea: DOWN 78 cents at US$54.84 per barrel
Oil - West Texas Intermediate: DOWN 63 cents at US$49.26