South Korea's Kospi dropped 3.5% to 2,098.37, while the S&P ASX/200 in Sydnay lost 2.3% to 6,978.30. Hong Kong's Hang Seng dropped 1.5% to 26,890.90 and the Shanghai Composite index lost 0.3% to 3,031.03. Benchmarks in Jakarta, Taiwan and Thailand fell by more than 1% and India's Sensex lost 1% to 40,766.94.
Japan's markets were closed for a holiday.
China's leaders promised more help for companies and the economy, saying they expect their growth targets can still be reached despite the outbreak.
At a news conference Monday, finance and planning officials said they are looking at how to channel aid to businesses after President Xi Jinping publicly promised over the past week to ensure farming and other industries recover quickly.
The government is looking at "targeted tax reduction," interest rate cuts and payments to poor and virus-hit areas, said an assistant finance minister, Ou Wenhan.
"We will do a good job of implementing large-scale interest rate reduction and tax deferral and ensure effective implementation as soon as possible," said Ou.
The viral outbreak that began in China has infected more than 79,000 people globally and killed more than 2,600 people. China has reported 2,592 deaths among 77,150 cases on the mainland.
Another large jump in new cases was reported in South Korea on Monday, a day after the the president called for "unprecedented, powerful" steps to combat the outbreak that is increasingly confounding attempts to stop the spread.
The 161 new cases bring South Korea's total to 763 cases, and two more deaths raise its toll to seven.
Hopes that the outbreak had been contained were premature, Mizuho Bank said in a commentary, "And indeed, fears of secondary infections proliferating outside of China have come home to roost, sending risk assets in a tailspin and a wave of refuge-seeking into safe-haven."
Stocks fell and bond prices jumped Friday on Wall Street amid signs the viral outbreak is weighing on U.S. companies.
The S&P 500 fell 1.1% to 3,337. The Dow Jones Industrial Average fell 0.8% to 28,992. The Russell 2000 index of smaller company stocks gave up 1.1%, while the tech-heavy Nasdaq lost 1.8% to 9,576.
Technology companies, which have much greater exposure to China than other industries, fell the most. Chipmakers, which rely heavily on China for both sales and supply chains, were some of the worst hit. Advanced Micro Devices slid 7%, while Nvidia fell 5.6%.
Data from IHS Markit show U.S. manufacturing and business activity slowed in February from the previous month, coming in below analysts' expectations.
Travel restrictions, business closures and other efforts in China aimed at containing the spread of the virus have begun to disrupt supply chains and sales prospects for Apple and other big companies.
Companies that depend on consumer spending, especially in travel-related industries, also fell broadly. Marriott International shed 2.7% and Carnival fell 1.8%. American Airlines dropped 3.2%. General Motors lost 2.2% and other automakers slipped as the virus hurts auto sales in China
The yield on the 30-year Treasury has dipped to record lows as investors sought the safety of U.S. government bonds. It fell to a record low of 1.886%, according to Tradeweb, from 1.98% late Thursday.
The yield on the more closely followed 10-year Treasury was at 1.47%. That yield, which is a benchmark for mortgages and other kinds of loans, was close to 1.90% at the start of this year.
The price of gold also rose, surging $15.70 to $1,664.50 per ounce.
Expectations have been building among traders that the Federal Reserve will need to cut interest rates this year to help the economy. They're pricing in a 90% probability of at least one cut this year, up from an 85% probability a day ago and a 58% probability a month ago.
Uncertainties are weighing on energy prices as well. Benchmark U.S. crude lost $1.22 to $52.16 per barrel in electronic trading on the New York Mercantile Exchange. It lost 50 cents to $53.38 per barrel on Friday.
Brent crude, the international standard, gave up $1.42 to $56.52 per barrel.
The U.S. dollar rose to 111.59 Japanese yen from 111.57 yen on Friday. The euro weakened to $1.0819 from $1.0847.