Tokyo's Nikkei 225 index lost 1.6%, bouncing back from bigger losses, to 40,134.97.
The Hang Seng in Hong Kong edged 0.2% higher, to 24,589.21, while the Shanghai Composite index was nearly unchanged at 3,562.18.
In South Korea, the Kospi surged 0.7% to 3,140.92.
Australia's S&P/ASX 200 shed 0.2% to 8,643.00.
Investors' worries about a weakening U.S. economy deepened after the latest report on job growth in the U.S. showed employers added just 73,000 jobs in July. That is sharply lower than economists expected. The Labor Department also reported that revisions shaved a stunning 258,000 jobs off May and June payrolls.
“The labor market, once a pillar of resilience, is now looking more like a late-cycle casualty, as soft data begin to replace soft landings in market discourse,” Stephen Innes of SPI Asset Management said in a commentary.
U.S. futures edged 0.3% higher, however, early Monday.
On Friday, the S&P 500 fell 1.6%, its biggest decline since May 21 and its fourth straight loss. It closed at 6,238.01, posting a 2.4% loss for the week.
The Dow Jones Industrial Average fell 1.2% to 43,588.58, while the Nasdaq composite fell 2.2% to finish at 20,650.13.
Internet retail giant Amazon fell 8.3%, despite reporting encouraging profit and sales for its most recent quarter. Technology behemoth Apple fell 2.5% after also beating Wall Street’s profit and revenue forecasts. Both companies face tougher operating conditions because of tariffs, with Apple forecasting a $1.1 billion hit from the fees in the current quarter.
Trump’s decision to order the immediate firing of the head of the government agency that produces the monthly jobs figures raised concern over whether there might be interference in future data.
The surprisingly weak hiring numbers led investors to step up their expectations the Federal Reserve may cut interest rates in September.
The yield on the 10-year Treasury fell to 4.21% from 4.39% just before the hiring report was released. That’s a big move for the bond market. The yield on the two-year Treasury, which more closely tracks expectations for Fed actions, plunged to 3.68% from 3.94% just prior to the report’s release.
The Fed has held rates steady since December. A cut in rates would give the job market and overall economy a boost, but it could also risk fueling inflation, which is hovering stubbornly above the central bank’s 2% target.
An update on Thursday for the Fed’s preferred measure of inflation showed that prices ticked higher in June, rising to 2.6% from 2.4% in May.
The Fed held rates steady again at its most recent meeting this week. Fed Chair Jerome Powell has been pressured by Trump to cut the benchmark rate, though that decision isn’t his to make alone, but belongs to the 12 members of the Federal Open Market Committee.
Businesses, investors and the Fed have been operating under a cloud of uncertainty from Trump’s tariff policy.
Companies have been warning investors that unpredictable policies, with some tariffs already in effect while others change or get extended, make it difficult to plan ahead. Walmart, Procter & Gamble and many others also have warned about import taxes raising costs, eating into profits and raising prices for consumers.
In other dealings early Monday, U.S, benchmark crude oil lost 18 cents to $67.15 per barrel. Brent crude, the international standard, fell 23 cents to $69.44 per barrel.
The U.S. dollar rose to 147.80 Japanese yen from 147.26 yen. The euro weakened to $1.1577 from $1.1598.