About 40 minutes into trading, the Dow Jones Industrial Average was at 25,138.14, up 0.9 percent.
The broad-based S&P 500 advanced 0.7 percent at 2,714.17, while the tech-rich Nasdaq Composite Index gained 0.3 percent to 7,138.35.
Key gainers included oil companies ExxonMobil and Chevron, both up more than 1.0 percent, and industrials including Boeing, which rose 2.1 percent.
After more than a year of tranquility and a steady upward climb, the violent market swings in recent days have reestablished volatility as a force in US stocks. The Dow on Tuesday finished up 2.3 percent after a lurch of almost 1,200 points between its peak and nadir during the day, following Monday's session which saw the biggest point decline on record.
President Donald Trump, who has frequently touted stock market records as evidence of his successes, rued this week's turmoil on Twitter.
"In the 'old days,' when good news was reported, the Stock Market would go up. Today, when good news is reported, the Stock Market goes down. Big mistake, and we have so much good (great) news about the economy!"
New York Federal Reserve Bank President William Dudley said the swings of the last few days would not affect monetary policy decisions, in part because stocks are still relatively high.
"If the stock market were to go down precipitously and stay down, then that would actually feed into the economic outlook, and that would affect my view in terms of what's the implications for monetary policy," he added.
"But so far this is a big story in the press, it's a big story for financial market participants, but I don't think it's a big story at all for central bankers."
Disney gained 0.7 percent after announcing it will launch a streaming sports programming service through its ESPN network and disclosing plans for additional "Star Wars" movies. Earnings in the fourth quarter jumped nearly 80 percent to $4.4 billion due to one-time gains associated with the US tax reform.
Wynn Resorts surged 8.8 percent after chief executive Steve Wynn announced he was stepping down following allegations of decades of sexual misconduct.