Global stock markets climbed Friday after Federal Reserve Chairwoman Janet Yellen eased investors’ concerns that last week’s decision to keep rates near zero had put off a rate rise for the foreseeable future.

In a speech on Thursday at the University of Massachusetts in Amherst, Ms. Yellen laid out a detailed case for raising interest rates later this year.

European markets climbed sharply at the open, rebounding from Thursday’s losses. The Stoxx Europe 600 was 3.0% higher in early trade, although it remained on track for a weekly decline.

Europe’s indexes were also catching up with U.S. markets, where shares pared losses late in the session.

Stock futures indicated a 0.9% opening gain for the S&P 500. Changes in futures aren’t necessarily reflected in market moves after the opening bell.

The picture in Asia was more mixed. Japanese stocks wavered as investors digested Ms. Yellen’s speech, but rebounded after a pledge by Japanese Prime Minister Shinzo Abe to strengthen the country’s economy. The Nikkei closed 1.8% higher. China’s Shanghai Composite fell 1.6%.

Shares around the world have fallen since the Fed stood pat last Thursday, with investors interpreting the central bank’s caution as the latest worrying sign about the state of the global economy. Many are anxious for the Fed to make a start on returning monetary policy to normal after years of rock-bottom rates.

“When the Fed didn’t hike everyone started to worry they knew something we didn’t know about the economy,” said Andreas Koester, head of asset allocation and currency at UBS Global Asset Management, which oversees $695 billion of assets.

“What we heard yesterday [from Ms. Yellen] was a confirmation that it was just a close call. They’re still on track,” he said.

Ms. Yellen’s speech also gave the dollar a boost. The euro weakened to $1.1143 against the buck, having climbed to nearly $1.13 on Thursday. The dollar climbed against the yen to ¥120.66.

Higher interest rates make a currency more attractive to investors.

The dollar is likely to extend gains as markets price in a rate rise during the fourth quarter, said foreign exchange strategists at BNP Paribas.

In Europe, shares in the auto sector led Friday’s rebound. A number of car makers had fallen sharply on Thursday as the emissions scandal enveloping Volkswagen AG threatened to spread.

BMW AG climbed 4.7%, and Daimler AG rose 4.1%. Volkswagen itself was 1.3% higher ahead of the expected announcement of Porsche chief Matthias Müller as its new chief executive.

Energy and mining shares also bounced back after heavy losses.

In commodity markets, Brent crude oil was marginally higher at $48.88 a barrel. Gold was down 1.0% at $1,142.20 a troy ounce.