New York,  US stocks closed sharply higher on Tuesday with the Dow up more than 11 per cent, notching its biggest one-day percentage gain since 1933 amid stimulus hopes.

The Dow Jones Industrial Average surged 2,112.98 points, or 11.37 per cent, to 20,704.91. The S&P 500 increased 209.93 points, or 9.38 percent, to 2,447.33. The Nasdaq Composite Index jumped 557.18 points, or 8.12 per cent, to 7,417.86, Xinhua reported.

All the 11 primary S&P 500 sectors closed noticeably higher, with energy up 16.31 per cent, outpacing the rest.

Investors hoped US lawmakers were close to an agreement on a massive economic relief package to cushion the damage by the COVID-19 pandemic.

Tuesday's historic rally followed Wall Street's yet another setback in the previous session, with the 30-stock index finishing down nearly 600 points despite the Federal Reserve's decisive efforts.

The US central bank announced on Monday a plan to purchase US treasuries and agency mortgage-backed securities with no limit to help markets function more efficiently amid coronavirus uncertainty.

On the data front, US private sector firms indicated a marked contraction in overall business activity in March following the escalation of the COVID-19 outbreak.

Flash US Services Purchasing Managers' Index (PMI) registered 39.1 at the end of the first quarter, down from 49.4 in February, London-based global information provider IHS Markit reported on Tuesday.

IHS Markit Flash U.S. Manufacturing PMI fell from 50.7 in February to 49.2 at the end of the first quarter.

The number of COVID-19 cases in the United States topped 50,000 as of 3 pm US Eastern Time on Tuesday (1900 GMT), according to the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University. The fresh figure reached 50,206 with 606 deaths, the CSSE said.