By Min Zeng and Saumya Vaishampayan 

A measured Federal Reserve policy statement reaffirmed expectations that the central bank will move cautiously on interest rates, shoring up demand for stocks and government bonds.

Many money managers expect the Fed as soon as September to raise its federal-funds rate for the first time since 2006. Wednesday's Fed statement didn't change that view, but it reinforced analysts' projections that further rate increases will likely be deliberate amid a sluggish global economic outlook, soft U.S. inflation and accommodative monetary policy around the globe.

Stocks have broadly rallied since the financial crisis, driven in part by easy monetary policy. Many investors say they expect stocks to remain buoyant as long as rates stay low, as returns likely will remain more appealing than on bonds.

The major U.S. stock indexes rose between 0.4% and 0.7% Wednesday. The perceived odds of a rate increase later this year, as reflected in the fed-fund futures market, were little changed.

"There was nothing...where the Fed clarified that it would be raising rates in September," said David Donabedian, chief investment officer of Atlantic Trust Private Wealth Management, which oversees about $27 billion. "If an impending issue has ever had time to be priced into the market, this is it," he said.

Investors said the Fed's signaling contrasts with an earlier policy change, the mid-2013 shift away from monthly bond purchases. Yields moved sharply higher in that episode, known as the "taper tantrum," reflecting in part investors' surprise at the pace of the Fed's change in stance. Few expect a broad bond selloff this time around, thanks to expectations that rates will rise slowly and to a level that won't soon choke off growth.

"What matters more is that the Fed has a different game this time," said John Bredemus, vice president at Allianz Investment Management, which has more than $600 billion in assets under management globally. "Treasury yields are not going to rise dramatically with a shallow path of tightening."

On Wednesday, following the release of the Fed's statement, bond prices pared earlier declines. The yield on the 10-year Treasury note was 2.279%, up from 2.252% Tuesday. Bond yields rise as prices fall.

Signs of calm in the bond market are evident in the so-called term premium that reflects the compensation investors demand to hold 10-year Treasury notes rather than a series of shorter-term notes.

The 10-year note's term premium hit 0.18 percentage point on Monday, down from 0.51 percentage point on June 26, the highest level since September, according to the latest data from the Federal Reserve Bank of New York. Two years ago, the premium was 1.26 percentage point.

"Treasury yields are now at a level that is much more in line with economic fundamentals, while yields in May of 2013 were very depressed, " said Erik Schiller, senior portfolio manager at Prudential Financial Inc.'s fixed-income unit, which has $560 billion in assets under management. Mr. Schiller said he would buy Treasurys if the 10-year note's yield rises close to 2.5%.

U.S. government debt has posted a total return of 0.65% this year through Tuesday, according to data from Barclays PLC. Total return includes price gains and interest payments.

Riskier assets have performed better this year. The S&P 500 stock index has returned 2.8% including price gains and dividend payments for this year through Tuesday, according to FactSet. Bonds sold by lower-rated U.S. companies, known as junk debt, have returned 1.22% over the same period.

On Wednesday, the Dow Jones Industrial Average advanced 121.12 points, or 0.7%, to 17751.39. The S&P 500 rose 15.32 points, or 0.7%, to 2108.57, and the Nasdaq Composite gained 22.53 points, or 0.4%, to 5111.73.

The stock gains were broad-based, with all S&P 500 sectors ending higher.

The Fed sounded a positive note on the U.S. economy Wednesday, such as using the word "solid" to describe gains in the labor market, said Jim Paulsen, chief investment strategist at Wells Capital Management.

That will increase the emphasis on the July jobs report, which will be released next week, he said. A strong report could increase expectations for an interest-rate increase in September, he added.

On the other side of the Atlantic, the Stoxx Europe 600 closed up 1%, building on Tuesday's 1.1% gain. The gains followed a rebound in Chinese shares after a three-day slump that had knocked 11% off the value of China's main stock index.

A handful of corporate reports also attracted attention. Gilead Sciences said Tuesday afternoon its two major hepatitis C drugs generated about $4.9 billion in sales in the second quarter, topping Wall Street estimates. The company again raised its guidance for net product sales for the year. Its shares rose 2.3%.

Twitter late Tuesday said its second-quarter revenue rose 61%, outpacing expectations. Still, the company remains unprofitable and showed almost no growth in core users. Its shares dropped 15%.

Write to Min Zeng at min.zeng@wsj.com and Saumya Vaishampayan at saumya.vaishampayan@wsj.com