The Dow Jones Industrial Average rose 63.86 points, or 0.17 percent, to 37,798.97. The S&P 500 dipped by 10.41 points, or 0.21 percent, to 5,051.41. The Nasdaq Composite Index lost 19.77 points, or 0.12 percent, to 15,865.25.
Eight of the 11 primary S&P 500 sectors ended in red, with real estate and utilities leading the laggards by losing 1.53 percent and 1.36 percent , respectively. Meanwhile, technology and consumer staples led the gainers by rising 0.23 percent and 0.07 percent, respectively.
Powell said that while inflation continues to make its way lower, it hasn't moved quickly enough, and the current state of policy should remain intact.
"More recent data shows solid growth and continued strength in the labor market, but also a lack of further progress so far this year on returning to our 2 percent inflation goal. The recent data have clearly not given us greater confidence, and instead indicate that it's likely to take longer than expected to achieve that confidence," he said. "That said, we think policy is well positioned to handle the risks that we face."
Powell added that until inflation shows more progress, "we can maintain the current level of restriction for as long as needed."
U.S. Treasury yields rose as Powell spoke. The benchmark 2-year note, which is especially sensitive to Fed rate moves, briefly topped 5 percent, while the benchmark 10-year yield rose 3 basis points to 4.657 percent, or the highest closing level since Nov. 6.
"People are trying to balance this two-sided narrative: U.S. economic growth, which looks really good, and at the same time the inflation picture and interest rates, which will eventually be problematic for the equity market," said James St. Aubin, chief investment officer at Sierra Mutual Funds in California.
Meanwhile, new housing data released Tuesday morning showed a sharp decline in housing starts for March, dropping by 14.7 percent to 1.3 million seasonally adjusted, annualized units, the biggest drop in four years. The previous month's figures have also been revised downward from 1.52 million to 1.45 million. Both single-family and multi-family units were lower than anticipated, with single-family units at 1.1 million and multi-family units at 299,000.
Bank earnings season continues Tuesday, with Morgan Stanley's stock gaining ground following a first-quarter profit that surpassed expectations, driven by a resurgence in income from investment banking. On the other hand, Bank of America saw its shares decline after reporting lower first-quarter profits, attributed to increased provisions for loan losses.
Johnson & Johnson experienced a slip in its stock value as the company's revenue fell short of analyst estimates, particularly due to lower-than-expected sales from its popular psoriasis drug Stelara.
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