The gains followed a strong finish to last week after robust US jobs data on Friday eased concerns about global growth. Signs over the weekend that Greece had made progress on its debt bailout program also bolstered sentiment.
Investors' nerves were soothed by comments from European Central Bank President Mario Draghi late last week on plans for a new wave of bond purchases aimed at helping to calm the euro zone's turmoil, lately focused on Spain and Italy's high borrowing costs.
"Investors are less pessimistic about the euro zone situation. There is the expectation that something positive will come out of the ECB plan and so investors are more willing to search for risky assets that look attractive," said Aroop Chatterjee, senior currency strategist at Barclays Capital in New York.
Inspectors from the International Monetary Fund, the European Commission and the European Central Bank - known as the troika - concluded a visit to Greece, saying they would return in September to give their final verdict.
They said Greece has made progress in finding budget cuts needed to continue its bailout program but cautioned that more work is needed.
The euro zone's problems remain the focus for many major investors, though tensions remain as details of exactly how the ECB will stabilize the bloc's bond markets have yet to be settled.
That lack of clarity warrants some caution from investors, said Kate Warne, investment strategist at Edward Jones in St Louis.
"We've seen time and time again great statements out of European leaders - they talk a great talk but they rarely follow through on the walk that's needed," said Warne.
"Usually they walk just far enough to keep the markets somewhat calm and I think we're seeing that again where Draghi's comments 10 days ago really calmed the markets but his lack of follow-through has led to more nervousness."
The MSCI World Index, which captures the world's biggest stock markets, was up 0.7% to its highest level since early May. The pan-European FTSEurofirst 300 ended up 0.4% at 1,085.79.
The Dow Jones industrial average gained 21.34 points, or 0.16%, to 13,117.51. The Standard & Poor's 500 Index rose 3.24 points, or 0.23% to 1,394.23. The Nasdaq Composite Index added 22.01 points, or 0.74% to 2,989.91.
The benchmark 10-year US Treasury note traded 03/32 higher in price to yield 1.560%.
The euro last traded 0.1% higher at $1.2400, below a one-month peak of $1.2443 hit in Asian trade. Gains in the euro over the last two days were nearly 2%, its best two-day showing since late October.
Spanish and Italian bond prices rose further, led by revived demand for shorter-dated paper on prospects of eventual ECB buying.
Spanish 10-year yields fell 14 bps to 6.8% retreating further from euro-era highs of 7.78% hit early last week, with equivalent Italian yields 6 bps lower at 6.0%. Two-year paper yielded 3.11%, down more than 20 bps on the day.
The ECB continued to keep a lid on its bond purchase program last week. The ECB has barely used the Securities Markets Program this year and has not bought any bonds in 21 weeks despite a severe intensification of the euro zone debt crisis.
Oil gained in thin, choppy trade, supported by higher equities but buffeted by ongoing turmoil in the Middle East.
NYMEX crude for September delivery rose 80 cents to settle at $92.20 a barrel.