Germany's DAX jumped 2% to 12,942.82 while the CAC 40 in Paris also gained 2%, to 5,008.60. Britain's FTSE 100 surged 1.8% to 6,161.97. The future contract for the S&P 500 climbed 0.5% to 3,368.60 while that for the Dow industrials rose 0.7% to 27,875.00.
Investors are looking to Washington for a fresh lifeline for the U.S. economy, which pancaked into recession as the pandemic gained ground in the spring.
On top of the rising number of coronavirus counts around the world, uncertainty has grown with widening antagonisms between the United States and China, the world's largest economies. The latest move in their escalating tensions was China's announcement of unspecified sanctions against 11 U.S. politicians and heads of organizations promoting democratic causes, including Sens. Marco Rubio and Ted Cruz.
The two sides are scheduled to hold virtual trade talks at the end of the week.
Overnight, the S&P 500 rose 0.3%, to 3,360.47, after wavering between small gains and losses. The benchmark index is now within 1% of its last record high.
A flood of government spending and monetary stimulus, with central banks buying assets to keep credit cheap, have kept markets rising since March.
"With the Fed buying credit and indirectly saving U.S. stocks, traders should not expect any major corrections even if the selling of tech stocks persists deeper into the trading week," Edward Moya of Oanda said in a commentary.
The Hang Seng in Hong Kong added 2.1% to 24,890.68, while the Nikkei 225 climbed 1.9% to 22,750.24. In South Korea, the Kospi picked up 1.4% to 2,418.67. Sydney's S&P/ASX 200 advanced 0.5% to 6,138.70, while the Shanghai Composite index gave up earlier gains, dropping 1.2% to 3,340.29.
India's Sensex gained 0.8% to 38,495.84.
The yield on the 10-year Treasury rose to 0.59% from 0.58%.
Benchmark U.S. crude oil for September delivery gained 38 cents to $42.32 per barrel in electronic trading on the New York Mercantile Exchange. It rose 72 cents on Monday to settle at $41.94 a barrel. Brent crude oil for October delivery picked up 30 cents to $45.29 per barrel. It rose 59 cents to $44.99 a barrel overnight.
The price of gold fell $44 to $1,995.70 per ounce.