By Anna Isaac

Global stock markets and U.S. futures rallied on hopes for a strong recovery from the coronavirus pandemic and a signal from Chinese state media suggesting investors should support a local bull market.

The Shanghai Composite Index gained 5.7% to reach 3332.88, its highest close since February 2018. Brokerages, banks, miners, aviation companies and developers led the rally. U.S. futures tied to the S&P 500 rose 1.3%. The pan-continental Stoxx Europe 600 climbed 1.3% with regional indexes in Germany and France among the strongest performers.

"In recent weeks the data has looked very positive from China. Its economy is back in motion, and that should lift global equities a bit," said Seema Shah, chief strategist at Principal Global Investors.

China market analysts said it was hard to pinpoint a single clear driver for Monday's surge, though some pointed to a front-page editorial in state-owned China Securities Journal. It said fostering a "healthy bull market" was important, given China's increasingly complicated international relations, intense financial and technological competition, and the challenge of controlling internal financial risks.

Investors compared the leap in Chinese financial markets to a wave of optimism that drove a historic bull run in 2014 and 2015 that eventually ended in a ruinous market crash.

"The article was a clear indication that China's government is determined to support the rally in local stocks. They're capable of doing that. They've proved that in the past by using state-owned entities to purchase local stocks," said Piotr Matys, foreign exchange strategist at Rabobank.

Rising coronavirus cases in the U.S. failed to deter investors Monday, as the figures were outweighed by the prospects for recovery and expectations for less stringent lockdown measures. A stronger risk appetite among traders helped push the U.S. dollar down 0.4% against a basket of major currencies, as measured by the WSJ Dollar Index.

"Very few people think that there will be as draconian lockdowns again," said James Athey, a senior investment manager at Aberdeen Standard Investments. "News on vaccines helps to minimize concerns."

Ahead of the opening bell in New York, shares of Uber Technologies rose 8.7% after it said Monday that it would buy Postmates for approximately $2.65 billion in an all-stock transaction. Shares in Becton Dickinson & Co. rose 4.3% premarket after the company said it was launching a rapid diagnostic test for the new coronavirus.

Chinese chip maker Semiconductor Manufacturing International said it plans to raise around $6.57 billion in a Shanghai listing. The company delisted from the New York Stock Exchange in June last year after trading there for 15 years.

In Germany, data showed that factory orders rebounded 10.4% in May after falling sharply during the lockdown in April. The increase was driven by both domestic and foreign orders, as economies around the world began to reopen. In other data released Monday, eurozone retail sales proved stronger than expected in May, outperforming economists' expectations by 14%.

Shares in Germany's second largest lender Commerzbank jumped 7.5% after the bank announced Friday that its chairman and chief executive would step down. The bank has been under pressure from one of its major investors, Cerberus Capital Management.

Across Europe the rally in equities was led by the financial, automotive and aerospace sectors. These companies were among those that would likely benefit most from a resurgence in economic activity, such as engine maker Rolls-Royce, and car-parts maker Faurecia, investors said.

Investors and traders will be paying close attention to the Institute for Supply Management's nonmanufacturing index, due out at 10 a.m. ET. The index is expected to show a small return to growth for the U.S. service and construction sectors in June. This would snap a streak of two months of shrinking in the sector, as the country has wrestled with coronavirus outbreaks.

In commodities, Brent crude futures, the international benchmark for oil prices, rose 1% to $43.23 a barrel. U.S. crude ticked down 0.1% to $40.63 a barrel.

The yield on the 10-year U.S. Treasury rose to 0.702% from 0.670% Thursday. U.S. markets were closed Friday for a public holiday.

Xie Yu contributed to this article.

Write to Anna Isaac at anna.isaac@wsj.com