NEW YORK, New York - Stocks ended sharply higher on Tuesday following mixed comments by Federal Reserve Chairman Jerome Powell.

Powell gave the strongest indication yet that the Fed believes inflation is coming down but foresaw interest rates possibly going higher and staying high for longer. He also warned rates could go higher than the market expects.

"The disinflationary process, the process of getting inflation down, has begun, and it's begun in the goods sector," Powell told the Economic Club in Wahington, DC, Tuesday. "But it has a long way to go. These are the very early stages of disinflation."

"The reality is we're going to react to the data," Powell said. "So if we continue to get, for example, strong labor market reports or higher inflation reports, it may well be the case that we have to do more and raise rates more than is priced in."

Powell's comments were well received by the markets, although stocks were volatile before settling on firm ground.

"He seems to reiterate the fact that, in his view, inflation is cresting. And that's been the biggest fear for participants in the market that with all the rate increases that, in the Fed's view, no real progress is being made against inflation," Rick Meckler, a partner with Cherry Lane Investments in New Vernon, New Jersey told Reuters Tuesday. "He's saying 'no, it's having its effect.'

Technology stocks led the charge, with the Nasdaq Composite surging 226.34 points or 1.90 percent to 12,113.79.

The Dow Jones industrials advanced 265.60 points or 0.78 percent to 34,156.62.

The Standard and Poor's 500 rose 52.90 points or 1.29 percent to 4,163.98.

The global financial markets were buzzing with activity following Powell's comments Tuesday, particularly in relation to foreign exchange rates. The euro to U.S. dollar exchange rate stood at 1.07206, approaching the U.S. close Tuesday, with a slight dip of 0.08 percent from its opening value.

The British pound to U.S. dollar rate has seen a positive change of 0.09 percent, currently at 1.20341. The U.S. dollar to Japanese yen exchange rate decreased by 1.08 percent to 131.187. The Swiss franc rate dropped by 0.59 percent to 0.92263. The U.S. dollar to Canadian dollar exchange rate also saw a decline of 0.23 percent to 1.34116.

The Australian dollar to U.S. dollar exchange rate saw a significant increase of 0.87 percent to 0.69443 Tuesday, while the New Zealand dollar firmed to 0.63162.

On global stock markets outside the U.S. Tuesday, several indices showed mixed results, with some major markets experiencing gains while others faced losses.

The FTSE 100 Index in the United Kingdom closed the day with a modest gain of 0.36 percent, while the DAX Performance Index in Germany saw a decline of 0.16 percent. The CAC 40 Index in Paris, France, also had a small decrease of 0.07 percent.

In Asia, Japan's Nikkei 225 Index saw a slight decline of 0.03 percent, while the Hang Seng Index in Hong Kong finished the day up by 0.36 percent. The SSE Composite Index in China had a positive day, closing with a 0.29 percent increase. The Shenzhen Index also saw gains of 0.12 percent.

Australia's S&P/ASX 200 Index saw a decrease of 0.46 percent, while the ALL ORDINARIES Index also saw losses of 0.42 percent. Meanwhile, the KOSPI Composite Index in South Korea had a positive day, finishing up by 0.55 percent.

In India, the S&P BSE SENSEX saw a decline of 0.37 percent, while the IDX Composite in Indonesia had a strong day, finishing up by 0.89 percent. The FTSE Bursa Malaysia KLCI saw losses of 0.95 percent, while the S&P/NZX 50 Index Gross in New Zealand saw a decrease of 0.56 percent.

Overall, it was a mixed day for global stock markets, with some indices showing improvement while others faced losses. Investors will be closely monitoring the markets in the coming days to see if this trend continues.