About 15 minutes into trading, the Dow Jones Industrial Average had gained 1.4 percent and stood at 24,537.98.
The broad-based S&P 500 was up 1.3 percent to 2,654.15, and the tech-rich Nasdaq Composite Index also advanced 1.3 percent to 6,965.55.
The early gains were a continuation of the positive momentum that closed Friday's trading after a topsy-turvy session that saw the Dow swing more than 1,000 points.
Still, analysts were guarded about the market's prospects. Sentiment has been pressured over the last 10 days or so by worries that the prospect of higher inflation will prompt the Federal Reserve to accelerate its interest rate hikes.
Rising interest rates could then draw investors out of stocks and into bonds.
"The markets appear to remain skittish as Treasury yields are mixed on the heels of a recent jump and some key inflation data later this week is expected to headline a fully-loaded economic docket," said a note from Charles Schwab.
Key economic releases include new data on consumer price inflation and retail sales.
Meanwhile, Trump is due to unveil proposals on infrastructure spending, as well as a federal budget that reportedly will scrap a longstanding Republican goal of eliminating the deficit.