At the close of U.S. trading, the Dow Jones Industrial Average finished up 0.91%, the S&P 500 index ended up 0.78%, while the Nasdaq Composite index rose 0.87%.
The Labor Department said earlier that the country's consumer price index in May rose 1.4% on year, in line with forecasts and up from 1.1% in April though below the Fed's 2.0% target.
Consumer prices rose 0.1% in May from April, slightly below expectations for a 0.2% increase.
Core inflation, which excludes food and energy costs, rose 0.2% in May from April, also in line with expectations.
The year-on-year core inflation rate came in unchanged at 1.7%
In a separate report, the Commerce Department said the number of building permits issued in the U.S. fell 3.1% in May to 974,000, outpacing expectations for a decline of 2.8% to 975,000 units.
U.S. housing starts rose by 6.8% last month to hit 914,000 units, below expectations for an increase of 11.4% to 950,000.
The data fueled expectations that the Fed will keep stimulus measures in play such as its USD85 billion asset-purchasing program for a while even if monetary authorities signal an exit strategy on Wednesday.
Stimulus tools tend to send stock prices gaining.
Leading Dow Jones Industrial Average performers included General Electric, up 2.40%, UnitedHealth Group, up 2.05%, and Verizon Communications, up 1.66%.
The Dow Jones Industrial Average's worst performers included Merck, down 0.08%, Microsoft, up 0.03%, and Procter & Gamble, up 0.09%.
European indices, meanwhile, finished mixed.
After the close of European trade, the EURO STOXX 50 fell 0.07%, France's CAC 40 fell 0.08%, while Germany's DAX 30 finished up 0.17%. Meanwhile, in the U.K. the FTSE 100 finished up 0.69%.
On Wednesday, all eyes will focus on the Federal Reserve and its announcement on monetary policy.