NEW YORK, New York - Bank shares sustained more damage on U.S. stock markets Tuesday but the selling somewhat abated. Moody's, however, put a dampener on markets by downgrading the banking sector to negative.

"We have changed to negative from stable our outlook on the U.S. banking system to reflect the rapid deterioration in the operating environment following deposit runs at Silicon Valley Bank (SVB), Silvergate Bank, and Signature Bank (SNY) and the failures of SVB and SNY," Moody's said Tuesday.

Despite the downgrade, U.S. stocks were in demand.

"It's a sigh-of-relief rally, we'll call it, given the lack of any major surprises in CPI and then just the lack of any surprises overnight in the banking space," Adam Turnquist, chief technical strategist at LPL Financial told CNBC Tuesday.

"The market's welcoming that."

The Nasdaq Composite did best, surging 239.31 points or 2.14 percent to 11,428.15.

The Standard and Poor's 500 jumped 54.80 points or 1.68 percent to 3,920.56.

The Dow Jones rose 336.26 points or 1.06 percent to 32,155.40.

It was a mixed day for the forex markets on Tuesday, as some currencies gained ground against the U.S. dollar, while others fell back.

The Euro/U.S. dollar pair closed at 1.07416, up 0.10 percent or 0.00106 from the previous day's close. Meanwhile, the U.S. dollar/Japanese yen pair rose by 0.74 percent or 0.979 to 134.152.

However, the U.S. dollar/Canadian dollar pair fell by 0.43 percent or 0.00594 to close at 1.36709. Similarly, the British pound/U.S. dollar pair closed down 0.04 percent or 0.00043 at 1.21777.

The U.S. dollar/Swiss franc pair had a positive day, closing up 0.21 percent or 0.00193 at 0.91299. The Australian dollar/U.S. dollar pair also gained ground, rising by 0.27 percent or 0.00181 to 0.66849.

Finally, the New Zealand dollar/U.S. dollar pair closed up 0.33 percent at 0.6237.

Overall, it was a day of mixed results for the forex markets, with some currencies gaining against the U.S. dollar while others fell back. Traders and investors will be keeping a close eye on these pairs in the coming days to see how they continue to perform.

As the closing bell rang on global stock markets Tuesday, the day's results were a mixed bag. The FTSE 100 in London had a strong showing, closing up 1.17 percent, with the German DAX PERFORMANCE-INDEX and the Paris-based CAC 40 following suit with gains of 1.83 percent and 1.86 percent, respectively.

However, the Nikkei 225 in Tokyo and Hong Kong's HANG SENG INDEX both suffered losses Tuesday, dropping by 2.19 percent and 2.27 percent, respectively. Meanwhile, China's Shanghai Composite Index and Shenzhen Index closed down 0.72 percent and 0.77 percent, respectively.

The Australian S&P/ASX 200, and AUSTRALIAN ALL ORDINARIES, and FTSE Bursa Malaysia KLCI all closed down as well, with losses of 1.41 percent, 1.50 percent, and 1.97 percent, respectively.

On the other hand, the ESTX 50 PR.EUR, Euronext 100 Index, and BEL 20 had positive gains of 2.02 percent, 1.62 percent, and 1.88 percent, respectively.

The MOEX Russia Index, STI Index, S&P BSE SENSEX, IDX COMPOSITE, New Zealand's S&P/NZX 50 INDEX GROSS, and South Korea's KOSPI Composite Index all had mixed results Tuesday, with some closing up and others down.

As traders and investors studied the day's closing numbers, it was clear that the markets were volatile and unpredictable. Some sectors and regions performed better than others, but overall, uncertainty continued to prevail in the global stock markets.