The Dow rose 410 points, or 1.7 percent, to 24,601.
Technology and industrial companies and retailers were leading the market higher Monday.
But some market analysts warned that Monday's quick rise in stock prices may be a sign that after more than a year of market calm, volatility but not necessarily optimism had re-emerged. As a result, the investors have their eyes on the bond market regarding interest rates with the yields dipping during the morning trade, Tuesday.
"The catalyst behind this bull market up until maybe the past year or so has just been the ability of this economy to grow, even if it's very sluggishly (.) without creating any negative consequences for the financial markets", he said.
The Nasdaq jumped 107.47 (+1.56 percent) to close at 6,981.96, while the S&P 500 finished trading at 2,656.00, up 36.45 (+1.39 percent) for the day. At the end the index closed with increase of or 1.70% to 24,601.27 points.
By 6:53 a.m. ET (1153 GMT), Dow e-minis were down 183 points, S&P 500 e-minis were down 17.25 points and the Nasdaq 100 e-minis were down 46.75 points.
It took just nine days for stocks to plunge 10 percent from their latest peak, which was reached on January 26.
Not only are corrections common during bull markets, they're seen as entirely normal and even healthy. According to LPL Financial, it was the swiftest move from a record high to a correction in the history of the S&P 500.
The broader Standard & Poor's 500, which many index funds track, rose 43 points, or 1.7 percent, to 2,663.
Stocks got off to a fast start, as expected, with early gains nearly reaching the quantities seen in the whole of Friday's session. Walgreens fell 1.8 percent. But it's happened six times in the last seven trading days, and eight times since the January 26 peak.
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On Monday, the Dow, comprising 30 well-known company stocks, surged with Boeing and Apple up more than 4 percent.
Investor attention is focused on the question of inflation.
US investors have been torn between enthusiasm for the tax cut passed by Congress previous year that could provide a stimulus to an economy already at full employment, and growing fears that interest rates will jump as the federal government borrows big to cover its growing deficits.
The three major indexes plummeted into correction last week - a 10% drop from recent peaks - after a long and unusually stable period that helped catapult them to record highs.
CSRA Inc (NYSE:CSRA), a provider of information technology services to the USA government, opened sharply higher, up nearly a third at US$40.49 after its board gave the green light to a takeover by General Dynamics Corp (NYSE:GD) worth US$40.75 a share. Trump also unveiled a plan to spend $1.5 trillion on the country's ailing infrastructure over the next decade. CSRA climbed $9.57, or 31.1 percent, to $40.39 Monday.
Twenty-First Century Fox picked up 66 cents, or 1.9 percent, to $36.40 after The Wall Street Journal reported that cable and internet provider Comcast is still interested in buying Fox's entertainment divisions and could make another offer. Disney agreed to buy Fox's movie and television studios and some cable and worldwide TV businesses in December for $52.4 billion.
Bond prices were little changed.
Treasurys sold off on Monday, with the yield on the 10-year note rising 5 basis points to 2.88%.
In other energy trading, wholesale gasoline fell 2 cents to $1.68 a gallon. Heating oil dipped 3 cents to $1.99 a gallon. Natural gas slid 3 cents to $2.55 per 1,000 cubic feet. The euro fell to $1.2276 from $1.2392. The futures on gold rose by 0.81% to 1,326.30 Dollars per ounce. Silver lost 20 cents, or 1.2 percent, to $16.14 an ounce. Hong Kong's Hang Seng index added 1.4 per cent to 29,884.06 and the Shanghai Composite Index advanced 1.0 per cent to 3,185.86.