 "World stocks rise, dollar slips")
Emerging markets were one of the biggest beneficiaries, having previously been under pressure as investors took funds away from those economies most reliant on external funding back into the recovering developed world.
Friday's data showed the US economy had its weakest monthly job growth in three years in December. This triggered a slide in US Treasuries, where benchmark yields posted their biggest one-day drop since October.
The report did not change expectations that the Fed would wind down its bond-buying programme by year-end, but interest rate futures markets pushed back the timing of the first rate hike towards late-2015 from mid-2015.
"The market is taking its leads from US Treasury markets, which are generally weighing on the dollar across the board," said Adam Cole, global head of FX strategy at RBC Capital Markets.
MSCI world equity index gained 0.2%, approaching a six-year high set last month, buoyed by a 0.7% gain in emerging stocks.
European stocks followed Asia higher to rise 0.3%, staying hear a 5-1/2 year peak. Japan was closed for a public holiday.
European banking stocks rose 1.2% after global banking regulators agreed on Sunday to ease a new rule on how banks' leverage ratios are calculated to try to avoid crimping financing for the world economy.
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"This is a good news because it will give banks some breathing space. There have been concerns that high ratios would hit banks' profitability," said Global Equities' head of quantitative sales trading David Thebault.
"The fact that euro zone assets lead the gains so far this year is a positive sign. It means that things have greatly stabilised and that the region is not a pariah for global investors as it used to be."
Investors will keep an eye on the fourth-quarter earnings season, with major US banks including JPMorgan , Citigroup and Goldman Sachs announcing results this week. European earnings will gather pace in the last week of the month.
Benchmark 10-year euro zone bond yields were slightly lower on the day while Bund futures prices rose 3 ticks.
The 10-year US yield was stable at 2.8635%, slightly above Friday's lows.
The dollar fell 0.7% to 103.24 yen, its lowest level in nearly a month, pulling further away from a five-year high of 105.45 yen set earlier this month.
In commodity markets, gold extended its rally to a one-month peak at $1,254.05 an ounce having climbed 1.5% on Friday.
Oil prices retreated after nations struck a six-month deal with Iran to curb its nuclear programme and US President Barack Obama urged Congress not to impose additional sanctions on the country. Nymex oil futures lost 0.6% Brent crude fell below $107 a barrel.