"Just because we removed the word patient from the statement doesn't mean we are going to be impatient," Chair Janet Yellen said in a press conference Wednesday in Washington.
In afternoon trading on Wall Street, the Dow Jones Industrial Average gained 0.81 per cent, while the Standard & Poor's 500 Index rose 0.87 per cent, and the Nasdaq Composite Index added 0.79 per cent.
Treasuries also rose, pushing yields on 10-year notes nine basis points lower to 1.96 per cent.
"This was largely what was expected, though some may have been fearing a more hawkish Fed, and that explains the rally we're seeing right now, that it didn't state a precise time for raising rates," John Carey, portfolio manager at Pioneer Investment Management in Boston, told Reuters.
Fed policymakers remain cautious.
"The Committee currently anticipates that, even after employment and inflation are near mandate-consistent levels, economic conditions may, for some time, warrant keeping the target federal funds rate below levels the Committee views as normal in the longer run," the Fed said.
In its latest forecasts, the Fed lowered its range for its GDP growth prediction for 2015 to between 2.3 per cent and 2.7 per cent, down from its December estimate for between 2.6 per cent and 3.0 per cent, and downgraded its estimates for 2016 and 2017 growth as well.
However, it also decreased its estimate for unemployment rates, now forecasting a rate of between 5.0 per cent and 5.2 per cent for 2015, down from its December estimate for between 5.2 per cent and 5.3 per cent. It also lowered its forecast for the median for the federal funds rate at the end of 2015 to 0.625 per cent compared with 1.125 per cent in December.
Gains in shares of Chevron and those of Microsoft, last up 2.8 per cent and 2.3 per cent respectively, led the Dow higher. Shares of Exxon Mobil also increased, last up 2.2 per cent.
In Europe, the Stoxx 600 Index ended the day with a 0.3 per cent gain from the previous close. France's CAC 40 Index inched 0.1 per cent higher. Germany's DAX fell 0.5 per cent.
The UK's FTSE 100 Index jumped 1.6 per cent after Chancellor of the Exchequer George Osborne upgraded the country's economic growth forecast. Osborne predicted the UK economy will expand 2.5 per cent this year and 2.3 per cent in 2016, up from December forecasts for 2.4 per cent and 2.2 per cent respectively.
Meanwhile Greek stocks and bonds dropped amid intensifying concern about the country's ability to satisfy its international lenders. Greece's ASE Index dropped 4.1 per cent, while yields on Greek three-year notes soared 171 basis points to 22.14 per cent, and yields on the nation's 10-year bonds jumped 46 basis points to 11.27 per cent.
International Monetary Fund officials told their euro-area colleagues that Greece is the most unhelpful country the organisation has dealt with in its 70-year history, Bloomberg reported citing two unidentified people familiar with the talks.