Following the figures, stock markets added to their gains while the dollar's weakness was sustained as investors think it's now unlikely that the Fed will start reducing its stimulus this year. Until the budget stalemate in Washington, many investors had thought the Fed would already be "tapering" the stimulus.
"From the Fed's standpoint, this morning's report reaffirms their position to hold monthly asset purchases steady at $85 billion a month and essentially takes tapering off the table for October and likely December as well," said Sterne Agee chief economist Lindsey Piegza.
In Europe, the FTSE 100 index of leading British shares was up 0.8 percent at 6,710 while Germany's DAX rose 1.1 percent to 8,963. The CAC-40 in France was 0.6 percent higher at 4,302.
In the U.S., the Dow Jones industrial average was up 0.6 percent at 15,481 while the broader S&P 500 index rose the same rate to 1,755.
The dollar was under pressure, particularly against the euro, on the prospect of a longer period of stimulus, which effectively leads to the creation of more dollars. Europe's single currency was up 0.7 percent at $1.3768, its highest level since Nov. 2011.
"A lack of tapering, which to an extent had previously been priced in, leads to further dollar weakness, something that I expect to continue in the coming months," said Craig Erlam, market analyst at Alpari.
The U.S. jobs data were the main focus of attention despite more U.S. earnings statements. Around 30 percent of the companies listed on the S&P are due to release third-quarter numbers this week. Tuesday's results were solid enough, with Whirlpool, Delta Air Lines and Netflix up sharply after reporting higher earnings.
Earlier in Asia, the mood was subdued, too. Japan's Nikkei 225 stock average closed up 0.1 percent at 14,713.25 and Australia's S&P/ASX 200 added 0.4 percent to 5,373.10. Seoul's Kospi gained 0.2 percent to 2,056.12. Hong Kong's Hang Seng shed 0.5 percent to 23,315.99 and China's Shanghai Composite Index was off 0.8 percent at 2,210.65.
In the oil markets, a barrel of benchmark New York crude was flat at $99.68. Oil closed below $100 a barrel Monday for the first time since early July as U.S. supplies keep rising and the risks of disruption to Middle East shipments subside.