Stocks mostly rose on Tuesday after U.S. President Donald Trump returned to the White House to complete his recovery from the coronavirus, though uncertainty remained over prospects for fresh economic stimulus.

Trump left the hospital after spending less than three days there, returning from Walter Reed National Military Medical Center to finish his treatment at home. His doctor, Navy Cmdr. Sean Conley, said the president remained contagious and would not be fully “out of the woods” for another week.

Signs of Trump's improved condition boosted markets in Asia and Europe following an overnight rally on Wall Street. The future contract for the S&P 500 rose 0.1% and that for the Dow industrials edged 0.3% higher.

Germany's DAX rose 0.6% to 12,903 and the CAC 40 in Paris gained 0.7% to 4,905. Britain's FTSE 100 rose 0.2% to 5,957.

In Asian trading, Japan’s Nikkei 225 climbed 0.5% to 23,433.73 and the Hang Seng in Hong Kong jumped 0.9% to 23,980.65. South Korea’s Kospi added 0.3% to 2,365.90.

Australia’s S&P/ASX 200 rose 0.4% to 5,962.10 after the central bank kept its policies basically unchanged. Also on Tuesday, the government announced a big spending financial blueprint for the next few years that will drive business investment and job creation while repairing pandemic damage to the economy.

The annual budget contains a wage subsidy designed to get unemployed young Australians back to work and brings forward planned income tax cuts. The result will be record debt in the current fiscal year through next June.

Markets fell after Trump's positive COVID test was reported Friday, tumbling on concerns that a White House victory for Democrat Joe Biden would mean higher taxes and tighter regulations for companies, which could drag down their profits.

Worries over flaring outbreaks of the coronavirus have raised the urgency of fresh stimulus but it’s unclear if the Democrats and Republicans will manage to reach an agreement.

Analysts said a Democratic sweep of the election would allay fears of prolonged conflict over its outcome. It could also raise the probability of a big government support plan for the economy, something that investors have been clamoring for since jobless benefits and other stimulus Congress approved in March expired.

House Speaker Nancy Pelosi told airline executives on Friday to stop the furloughs of tens of thousands of workers because aid for the industry was “imminent,” either as a stand-alone effort or as part of a wider rescue package. A stand-alone bill for airlines failed to advance in the House on Friday, but hopes remain for a larger effort.

“Expectations are undeniably rising that compromise will be reached. With the FOMO (fear of missing out) gnomes of Wall Street piling into everything, I dread to the see the correction if they don’t though," Jeffrey Halley of Oanda said in a commentary.

U.S. benchmark crude oil picked up 76 cents to $39.98 per barrel in electronic trading on the New York Mercantile Exchange. It surged $2.17 on Monday to $39.22 per barrel. Brent crude, the international standard, gained 78 cents to $42.07 per barrel.

In currency dealings, the dollar weakened to 105.61 Japanese yen from 105.73 yen. The euro fell to $1.1798 from $1.1786.