By Joe Wallace and Chong Koh Ping

U.S. stock futures drifted lower Tuesday, following the biggest rally in blue-chip shares in over a month.

Futures tied to the Dow Jones Industrial Average edged down 0.6%, suggesting the benchmark U.S. index may halt gains sparked by signs of progress toward making a vaccine for the coronavirus. The Dow jumped 3.9% Monday in its biggest advance since April 6. The Stoxx Europe 600 ticked down 1.1%.

"Investors are just pausing for a breather after yesterday's excitement about the potential development of a vaccine," said Hugh Gimber, strategist at J.P. Morgan Asset Management. A successful vaccine would clear the way for a faster recovery in economic growth, he said, but "clearly there's a long way to go before that would come into practice."

In Europe, bond investors cheered signals that there might be momentum building among leaders to back a sweeping economic recovery plan. German Chancellor Angela Merkel and French President Emmanuel Macron late Monday proposed establishing a EUR500 billion ($546 billion) recovery fund to support regions worst hit by the coronavirus pandemic.

European officials have warned in recent weeks that more action is needed. A two-speed recovery across the region could entrench the differences between the EU's stronger northern economies and the hardest-affected countries in the bloc's south.

While the recovery fund needs the support of all 27 European Union members, "it would be a big game changer in terms of the perception of where the eurozone is headed," said James McCormick, head of desk strategy at NatWest Markets. "That's a big story."

The proposal boosted appetite for government bonds from debt-laden nations in southern Europe. The yield on 10-year Italian bonds fell to 1.636%, from 1.697% Monday. The spread, or extra yield that investors demand to hold Italian debt over German bunds, which are considered among the safest assets, narrowed. Yields on Spanish bonds slipped to 0.650%, from 0.742%. The 10-year Portuguese yield fell to 0.731%, from 0.83%.

The euro rose 0.3% against the dollar.

Ahead of the opening bell in New York, shares in Expedia Group fell 6% after analysts at Jefferies Group downgraded the travel company's stock and cut their target for the price. Shares in Marathon Oil slipped 4.4% after Moody's Investors Service said the outlook for the oil-and-gas company's credit rating was negative, citing low energy prices.

In Washington, Federal Reserve Chairman Jerome Powell plans to tell lawmakers on Tuesday that the central bank will use its " full range of tools to support the economy" as a result of the economic shock caused by the coronavirus pandemic. Mr. Powell didn't announce any new programs in his testimony, prepared for delivery to a congressional panel at 10 a.m. ET.

Treasury Secretary Steven Mnuchin said he expected economic conditions to improve in the second half of the year in his prepared testimony, which was released Monday afternoon. The yield on the 10-year U.S. Treasury note slipped to 0.714%, from 0.741% Monday.

Meanwhile, the recovery in oil prices signals that the Chinese economy is gathering momentum after slowing sharply at the start of 2020, said Mr. McCormick. That rally paused Tuesday as Brent-crude futures fell 0.6% to $34.61 a barrel. The global energy benchmark has advanced 31% in May.

Most major Asian benchmark indexes closed higher, as promising results in an early trial of Moderna Inc.'s coronavirus vaccine buoyed investors' optimism. Still, investors cautioned that the results of Moderna's trial were preliminary, and that the company's experimental vaccine has a lot to prove.

Japan's Nikkei 225 climbed 1.5% and South Korea's Kospi Composite added 2.3%.

"The markets are positive on the vaccine news because it will help eradicate the concerns of a resurgence," said Eddy Loh, senior investment strategist at Maybank Group Wealth Management in Singapore. Markets will fluctuate until there was more evidence that vaccines were effective, he added.

Mainland Chinese markets lagged behind regional peers, with the Shanghai Composite closing 0.8% higher. Investors in China are focusing on the country's coming annual legislative meetings, said Lee Kian Soon, chief executive officer at Astral Asset Management in Singapore.

Premier Li Keqiang is due to present China's spending plans for the year at the meetings, which start Friday. Chinese markets will rally if he unveils a large stimulus package to boost the economy, Mr. Lee said.

Write to Joe Wallace at Joe.Wallace@wsj.com and Chong Koh Ping at chong.kohping@wsj.com