By Min Zeng 

The yield on benchmark U.S. government bonds tumbled to the lowest level since May 2013 on Friday as global-growth worries struck close to home.

The bond market posted the biggest monthly price gain in more than three years, extending a rally over the past 12 months. Strong demand for haven bonds underscores investors' concerns over an uncertain global economic outlook and deflation risks in Europe.

Investors sought the relative safety of Treasurys after a report showed slower-than-expected fourth-quarter growth in the U.S. The slowdown cast doubt on the ability of the world's largest economy to withstand headwinds from sluggish growth in Europe and Asia.

Adding to the anxiety is a constellation of factors including ongoing political turmoil in Greece and renewed signs of instability in Russia's currency. Although it's still the early days of 2015, the sustained rally in Treasurys is defying the expectations of many Wall Street strategists for a rise in bond yields this year. Bond yields fall when prices rise.

"A slowdown in global and domestic economies will continue to fuel the Treasury bond rally," said Sean Simko, head of fixed-income management at SEI Investments in Oaks, Pa., which has $249 billion in assets under management. "The 10-year Treasury yield could continue its move into uncharted territory if the growth outlook deteriorates."

The scramble for a haven sent the yield on the benchmark 10-year Treasury note to as low as 1.651% during Friday's session, according to data provider Tradeweb. That's the lowest intraday level since May 3, 2013.

The yield on the 10-year Treasury note settled at 1.679% Friday afternoon, compared with 1.755% Thursday. The 30-year Treasury bond yield closed at a record low of 2.257%.

The 10-year yield tumbled by almost half of a point in January, the most on a monthly basis since August 2011.

Treasury bonds have posted a total return-including price changes and interest payments-of 2.19% this year through Thursday, the best monthly performance so far since August 2011, according to data from Barclays PLC. The return was 5.05% in 2014.

U.S. gross domestic product expanded at a 2.6% annual rate in the fourth quarter, the Commerce Department said Friday. Not only was that half the 5% pace of expansion in the third quarter, it fell short of the 3.2% rate of growth forecast by economists surveyed by The Wall Street Journal.

While U.S. indicators, especially of the labor market, have largely been rosy, some readings are prompting investors to reassess the resilience of the U.S. economy. The disappointing GDP report follows Tuesday's weak reading on durable-goods orders.

Across the Atlantic on Friday, Russia's central bank cut interest rates unexpectedly, fueling a selloff in ruble. The eurozone's annual inflation rate fell by 0.6% this month, the biggest decline since July 2009 and added to worries about deflation. Falling prices could cause consumers to hold back on purchases in anticipation of even lower prices in the future, potentially creating a cycle that could damage the economy.

Helping to fuel the four-month rally in the Treasury market is the European Central Bank, which last week announced a massive bond-purchase program in a bid to shore up growth on the Continent. Investors snapped up eurozone government bonds in anticipation of the program, driving yields to record lows in many countries. That bolstered the allure of Treasurys and other developed-country government bonds, as investors clamored for higher yields outside the eurozone.

On Friday, the yield on the 10-year German government bond closed at a record low of 0.302%, compared with 0.356% on Thursday, according to Tradeweb. The yield on the 10-year U.K. government bond also settled at a record low of 1.337%, compared with 1.421% on Thursday, according to Tradeweb.

Lower Treasury yields could be a boon for the U.S. housing market as they push down mortgage rates. Companies also benefit by locking in favorable borrowing costs when selling new debt.

But lower yields mean investors have to make do with less income, pushing many toward riskier bonds with higher yields. Some investors caution that bond buyers may be vulnerable if sentiment sours, as slim yields offer a thin layer of protection against the risk of capital losses.

"There is little margin for errors with yields so low," said David Keeble, global head of interest-rates strategy at Crédit Agricole in New York. "Any change in sentiment on the eurozone's growth or inflation outlook, U.S. bond yields could see a rapid pace of increase."

Others continue to believe bond yields have room to fall, at least in the short term.

Todd Hedtke, vice president of investment management for Allianz Investment Management, which manages over $600 billion in assets globally, said U.S. bonds "remain attractive" in a low-yield world.

"We are still buyers of Treasury bonds," said Mr. Hedtke. He declined to offer an exact forecast but didn't rule out the 10-year yield falling below 1.5%.

The 10-year U.S. bond yield closed at a record low of 1.404% in July 2012 when global financial markets were roiled by the eurozone's sovereign-debt crisis.

COUPON  ISSUE   PRICE      CHANGE   YIELD     CHANGE 
5/8%    2-year 100 2/32    up 3/32  0.472%     -4.8BP 
7/8%    3-year 100 10/32   up 6/32  0.768%     -6.4BP 
1 5/8%  5-year 100 10/32   up 15/32 1.187%     -9.6BP 
2 1/8%  7-year 100 1/32    up 18/32 1.495%     -8.7BP 
2 1/4%  10-year 105 4/32   up 22/32 1.679%     -7.9BP 
3%      30-year 116 6/32   up 1 20/32 2.257%   -6.9BP 
2-10-Yr Yield Spread: +120.7BPS +123.5BPS 
 
Source: Tradeweb/WSJ Market Data Group 

-- Write to Min Zeng at min.zeng@wsj.com