The Nasdaq composite, which is heavily weighted with technology stocks, climbed 32.97 points, or 0.4 percent, to 7,591.03. The S&P 500 rose 31 points, or 1.1 per cent, to 2,774, while the Nasdaq jumped 116 points, or 1.6 per cent, to 7.525.
The S&P 500 last week registered its biggest decline since the end of 2018 after tepid job and other economic data, but the index is up about 11 percent for the year so far.
The world's largest planemaker, which is the best performing Dow component this year by a wide margin, fell as much as 13.4% on Monday and weighed on the Dow Jones index.
The S&P 500 index rose 12 points, or 0.4 per cent, to 2,803.
Boeing briefly dipped, but finished slightly higher, after the US said it was joining other countries in grounding the company's 737 Max 8 airplane following a fatal crash of an Ethiopian airliner over the weekend.
Technology and health care stocks did the most to push the market higher Tuesday.
Stocks are opening mostly higher on Wall Street, led by gains in technology companies and banks.
Bond prices rose. The yield on the 10-year Treasury note fell to 2.63 percent.
"Lower rates help hold stocks up because (they) allow for higher multiples", said Bucky Hellwig, senior vice president at BB&T Wealth Management in Birmingham, Alabama. The Consumer Price Index for All Urban Consumers (CPI-U) increased 0.2 percent on a seasonally adjusted basis, the US Labor Department said on Tuesday. A key sales figure fell 2.2 percent in the period, worse than what analysts were expecting. London's FTSE 100 was also flat, at 7,156, while the pound dropped a sharp 1 percent on expectations that the latest version of Britain's Brexit deal with the European Union will be voted down by lawmakers on Tuesday.
CURRENCY: The dollar gained to 111.26 yen from Monday's 111.21 yen.
The Dow Jones Industrial Average was down 96.22 points, or 0.38 percent, to 25,554.66 on Tuesday. The euro rose to $1.1297 from $1.1240.
The price of gold rose 7 cents to $1,291.10 an ounce, silver rose 14 cents to $15.41 an ounce and copper rose 3 cents to $2.93 a pound.
The Dow is up 2,227.20 points, or 9.5 per cent.
The Russell 2000 is up 27.95 points, or 1.8 per cent.
A worker stands near the screen showing the Korea Composite Stock Price Index (KOSPI) at the Korea Exchange in Seoul, South Korea, Tuesday, March 12, 2019.
Crude oil futures settled higher for a second straight session on Tuesday, 12 March 2019 giving up an earlier move toward 2019 highs.