S&P 500 futures added 1.4 percent as of 11:24 a.m. in London, while the Stoxx Europe 600 Index rose 0.6 percent, extending a three-day, 6.7 percent jump. The S&P 500 had climbed as much as 0.6 percent on Oct. 7 on the back of the jobs numbers before being erasing gains after Fitch Ratings downgraded the foreign and local currency long-term issuer default ratings for Spain and Italy.
The euro advanced 1.6 percent against the dollar and strengthened 1.5 percent versus the yen after German Chancellor Angela Merkel said European leaders will do "everything necessary" to ensure that banks have enough capital.
The 103,000 gain in September payrolls announced by the Labor Department was more than economists had forecast and followed an upwardly revised gain of 57,000 for August. Private employment climbed 137,000 and included the return of 45,000 striking workers at Verizon Communications Inc.
"The continued forward momentum in private job growth should ease concerns that the U.S. will slip into recession in the second half of this year," said Michael Feroli, chief U.S. economist at JPMorgan Chase & Co. in New York.
The latest numbers bring the jobs data in line with what other statistics are suggesting: Gross domestic product is growing "very slowly," not contracting, he said.
Construction spending rebounded in August, propelled by the biggest jump in state and local government outlays in more than two years. Manufacturing accelerated in September, helped by gains in exports and production.
"For the first time in eight months, we revised upward our forecast of GDP growth over the second half, to just shy of 2.5 percent," economists at St. Louis-based Macroeconomic Advisers said in a report last week. In September, they were predicting second-half growth under 2 percent.
The drags on the economy in the first half of the year -- higher gasoline prices and supply-chain disruptions from the earthquake and tsunami in Japan -- are dissipating, giving growth a lift, Feroli said.
The average price for unleaded gasoline fell almost 20 cents, or 5.4 percent, in September to $3.43 a gallon, according to AAA, the nation's largest motoring group.
The automobile industry has been an obvious beneficiary. Car and truck sales rose to a seasonally adjusted annualized rate of 13.1 million in September, according to Autodata Corp. That's the highest since April's 13.2 million, when lost output caused by the tsunami started restraining supply.