By Min Zeng 

Investors are scrambling for the safety of U.S. government bonds, which in January notched the biggest monthly price gain in three years, as heightened worries about global growth spread to the U.S.

The yield on the 10-year Treasury note tumbled to its lowest level since May 2013 on Friday following a disappointing report on fourth-quarter U.S. growth, defying widespread expectations for bond yields to turn higher this year. The 10-year yields was 1.679% on Friday, down from 2.173% at the end of last year and 3.03% at the end of 2013.

Many investors now say Treasury yields, which move inversely to prices, have further to fall, citing not only uncertainty about the U.S. economy but also the drag from plummeting eurozone bond yields. Government bond yields across Europe have plunged to record lows, with some even breaking into negative territory, as the European Central Bank prepares a massive stimulus program to encourage growth and inflation on the Continent. Political turmoil in Greece has revived fears over a repeat of the 2010-2012 sovereign-debt crisis there.

It isn't only the health of the global economy that investors are uneasy about. Further stoking their appetite for relatively safe debt are the lackluster performance of U.S. stocks this year, a plunge in oil prices and turmoil in currency markets stemming from surprise central-bank actions.

Developments now unfolding in the bond market are reminiscent of this time last year. Yields at the start of 2014 unexpectedly fell as a severe winter crimped growth in the U.S., wrong-footing investors who believed that an improving labor market and a winding down of the Federal Reserve's bond-buying program would cause yields to rise.

What many investors and Wall Street strategists failed to anticipate this time was the sheer size of the ECB bond-buying program announced last week. Money managers scooped up European government debt ahead of the announcement that the central bank would purchase at least EUR1 trillion ($1.13 trillion) worth of bonds, and kept on buying in the wake of it.

"This hasn't been a made-in-America bull run," said David Rosenberg, chief economist and market strategist for Gluskin Sheff & Associates, a wealth management firm in Canada with C$8 billion ($6.3 billion) assets under management. "The bond bears got it wrong for focusing more on domestic growth developments but it has been the spillover from the yield meltdown in Europe that has dominated."

Traders said the buying on Friday was broad based, ranging from European money managers looking to snap up higher yields to U.S. investors buying debt to match month-end adjustments by big bond indexes.

On Friday, the yield on the 10-year German government bond closed at a record low yield 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.

A number of big banks on Wall Street still expect bond yields to rise at the end of this year, though some of them have lowered their prediction of how high yields could rise.

Bank of America Corp. expects the 10-year Treasury yield to rise to 2.35% at the end of December, down from 2.75% predicted last month. Barclays expects the yield to rise to 2.25%, down from 2.85% predicted in November last year.

Treasurys handed investors a return of 2.19%, counting both price increases and interest payments, in January, according to Barclays PLC data through Thursday. That is the best monthly performance since August 2011. For only the 10-year Treasury, the return clocked in at 3.9%, according to Ryan ALM. In contrast, most major U.S. stock indexes are down for the first month of the year.

To be sure, a surprise acceleration in global growth this year could make riskier assets such as stocks more attractive, causing investors to shed safe-haven investments like Treasurys.

Roaring prices have delivered strong capital gains for bond buyers. But lower yields mean buyers now have to make do with less income from interest payments.

"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. If there is "any change in sentiment on the eurozone's growth or inflation outlook, U.S. bond yields could see a rapid pace of increase."

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.

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.

The disappointing GDP report follows Tuesday's weak reading on durable-goods orders.

Across the Atlantic on Friday, the eurozone reported its annual inflation rate fell by 0.6% this month, the biggest decline since July 2009, adding 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.

"A slowdown in global and domestic economies will continue to fuel 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 growth outlook deteriorates."

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 eurozone's sovereign-debt crisis.

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

Corrections & Amplifications

Russia's central bank cut interest rates on Friday. A previous version of this story misstated the day of the week. (Jan. 30, 2015)