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Friday's disappointing data pulled down bond yields and the dollar, while lifting prices for gold and many commodities. It was also seen as beneficial for some emerging market countries which had been pressured by funds flocking to western assets.
While activity was curbed by a Japanese holiday, South Korea managed a rise of 0.7% and MSCI's broadest index of Asia-Pacific shares outside Japan added 0.6%. Emerging markets fared well with the Philippines up 1.7% and Indonesia more than 2%.
But Shanghai went flat after China set its yuan at a record high for a second straight session, extending the gradual appreciation of the currency.
Most other currencies in the region gained on the US dollar which skidded to 103.33 yen, having shed a full yen on Friday to end at 104.08 in New York.
The euro firmed to $1.3682, compared to $1.3590 before the job figures hit dealing screens on Friday. The Australian dollar also got a leg up to $0.9038, its best level in over a month.
Dealers said the market had been very long of dollars in anticipation of a strong US jobs number, in part due to a healthy reading from private payroll operator ADT.
Instead, payrolls rose just 74,000 in December, the smallest increase in nearly three years and far below the 196,000 forecast.
The jobless rate fell sharply to 6.7% though largely because of a fall in the participation rate as people dropped out of the labour force.
Still, the unemployment rate is now very close to the 6.5% threshold the Fed had nominated as a level where it might start considering raising interest rates.
More recently the central bank has watered down that threshold, saying it would keep rates near zero well past the time when the jobless rate slips under 6.5%.
Markets took the weakness of payrolls growth as adding to the case for keeping rates low for longer and pushed out the expected timing of the first hike. A move to 0.5% is now fully priced-in by August 2015.
Yields on 10-year Treasury paper were down at 2.85% after diving 10 basis points on Friday.
Yet the general assumption among economists was that the jobs report would not sway the Fed from winding down its bond buying campaign.
"Optimism that employment growth was beginning to take off has been dashed, at least for now, but we do not think the data suggest the economy is much weaker than we had thought," said RBS chief economist Michelle Girard.
"Thus, we do not think the Fed will alter the pace of tapering. We still expect the Fed to announce another $10 billion reduction in the monthly purchase pace at the January meeting."
There will be plenty of opportunity this week to hear from the Fed itself with seven separate appearances in the diary for officials, including Chairman Ben Bernanke on Thursday. Fed Bank of Atlanta President Dennis Lockhart gets the ball rolling with a speech later on Monday.
Also due this week are figures on US retail sales and on inflation in both the United States and Europe.
In commodity markets, gold extended its rally to a one-month peak at $1,254.05 an ounce having climbed 1.5% on Friday.
The price for nickel gained as a ban on unprocessed nickel laterite ore exports from top producer Indonesia came into effect, fanning a technical rally across other metals.
Nickel futures were up 0.9%, on top of a 3.8% jump on Friday.
Oil prices retreated after a rally on Friday. Nymex oil futures eased 40 cents to $92.32, while Brent crude oil futures lost 17 cents to $107.08 a barrel.
There was little reaction as yet to news of a deal for Iran to freeze parts of its nuclear programme in return for sanctions relief that will take effect on January 20. Iran will receive some easing of economic sanctions, including the suspension of restrictions on exports of petrochemicals.
