Stocks climb, erasing their losses for a tumultuous week.

Investors pushed past Russia’s invasion of Ukraine to focus on a sliver of good news on Friday: that President Vladimir V. Putin might engage in talks with his Ukrainian counterpart. That hope drove stocks up, and the S&P 500 closed a rollercoaster week with a gain.

The S&P 500 rose 2.2 percent, its best day in nearly a month, bringing it to a gain of 0.8 percent for the week after two consecutive weeks of losses. New data released on Friday showing that a key gauge of inflation had hit a new 40-year high in January also didn’t deter investors.

Friday’s gains echoed trading in Europe and Asia after the Kremlin said that Mr. Putin was willing to hold talks with Ukraine — although the Russian president later suggested he was not seriously planning to engage in them. The Nikkei in Japan closed nearly 2 percent higher, and the Stoxx Europe 600 rose more than 3 percent.

Equities are “a totally sentiment-driven market at the moment,” said Ross Mayfield, an investment strategy analyst at Robert W. Baird in Louisville, Ky. “Any hint that there could be talks or diplomatic resolution are going to move markets meaningfully.”

Oil prices continued their gyrations. Brent crude, the international benchmark, fell 1.2 percent to $97.93 a barrel, rebounding from an earlier drop of 2 percent. Oil had surged as high as $105 a barrel on Thursday, then eased back under $100 after President Biden said the United States was working with other countries to coordinate the release of supplies from petroleum reserves. West Texas Intermediate, the U.S. benchmark crude, was down as well, to $91.59 a barrel on Friday.

Markets had been whipsawed for weeks by the potential for war in Ukraine, with two back-to-back weeks of losses. Last week, investors sold their holdings heading into the holiday weekend as the United States delivered dire warnings that an invasion could be coming, leading to a two-day drop of 2.8 percent.

On Tuesday and Wednesday, stocks continued their fall as Mr. Putin ordered troops into two breakaway regions of Ukraine and the West began to announce sanctions for Russia. On Thursday, the S&P 500 started with a sharp decline after Russia began airstrikes of major Ukrainian cities, but it eventually shrugged off its early losses and closed with a 1.5 percent gain.

Investors have been grappling with the invasion’s potential implications for air travel in the region, banking in Europe and already raging global inflation, among other worries. Those concerns have helped push the S&P 500 and the Stoxx Europe 600 down more than 7 percent so far this year — their worst stretch since the start of the coronavirus pandemic in early 2020.

The potential for talks between Russia and Ukraine helped an index of bank stocks climb 4 percent Friday, trimming a five-day slide. Airline stocks also rebounded. Shares of Delta Air Lines and American Airlines were up 3 percent.

The recent jump in energy prices is sure to worsen inflation, which had already been troubling policymakers and stock investors around the world. Central banks like the Federal Reserve are committed to raising interest rates to cool the economy, but the conflict could also hurt growth (a reason not to raise interest rates), introducing more uncertainty about the outlook for both prices and the economy for investors.

“The implications of the unfolding situation in Ukraine for the medium-run economic outlook in the U.S. will also be a consideration in determining the appropriate pace at which to remove accommodation,” Loretta J. Mester, president of the Federal Reserve Bank of Cleveland, said in a speech on Thursday.

Sanctions, too, will ripple across the global economy. On Thursday, Mr. Biden said the United States would cut off Russia’s largest banks and largest companies from Western financial markets and restrict exports of technology to Russia. He also said the United States was freezing trillions of dollars in Russian assets, including the funds controlled by Russian elites and their families. European leaders agreed on Friday to another round of sanctions aimed at the Russian economy and Mr. Putin himself. Western powers have left room to impose more severe economic penalties should the conflict escalate further.

The fighting in Ukraine has spurred volatility in the short term, but the long-term economic impact for American investors may be more muted, said Kristina Hooper, the chief global market strategist at Invesco.

“Many investors do look at this with a historical perspective and recognize, while conflicts can be horrible in terms of human toll, typically they don’t have a real scarring impact” on markets and the economy, she said.