Fresh fears have been raised about the economic outlook after the US economy lost momentum at the end of last year and the eurozone descended deeper into deflation.

Figures from the European statistics office, suggesting that prices fell 0.6% in January on the previous year, the biggest drop since the depths of recession in 2009, prompted warnings that radical action by the European Central Bank may have come too late to shore up the eurozone’s flagging recovery.

Meanwhile in the US, growth slowed sharply in the final quarter as weak business spending and a growing trade deficit offset strong consumer spending. GDP rose an annual 2.6%, almost half the 5% rate of the third quarter. Economists had expected that growth in the world’s biggest economy would slow in the final three months of the year, but not so sharply, with the consensus forecast for 3% expansion.

The GDP figures combined with worries about the eurozone to push shares down on Wall Street.

“The slowdown was bigger than expected and feeds into fears that a strong dollar, an international slowdown and slowing investment in the US oil industry will take a toll on US growth,” said Jasper Lawler, market analyst at CMC Markets UK.

Economists also noted pressures on the US and wider global economy from worries about the stability of the eurozone, a key trading bloc, after Greek anti-austerity party Syriza took power in the country that first sparked the eurozone debt crisis.

“Escalating tensions with Russia and the potential for another flare-up of the euro area debt crisis following the anti-austerity Syriza party’s success in the Greek elections remain key risks to the global economic outlook,” said Chris Williamson, chief economist at the data company Markit, which publishes surveys on economies around the world.

But he highlighted that consumer confidence remained strong in the US and that in Europe there was also a potential boost for business and consumer confidence from the ECB’s announcement that it is to begin pumping €1.1tn of extra money into the economy through quantitative easing (QE).

The bank’s chief, Mario Draghi, has said he will begin the money-printing programme in March in a move to tackle deflation and prevent the fragile eurozone economy from grinding to a halt as slumping prices encourage businesses and consumers to put off spending.

The move appeared to be vindicated on Friday by news that deflation was sharper than expected in January, driven in part by a slump in oil prices. The 0.6% annual drop in consumer prices across the single currency bloc matched a record fall set in July 2009. It follows annual deflation of 0.2% in December and was worse than the forecast of a 0.5% fall in a Reuters poll of economists.

Even core inflation, which strips out the effect of falling oil prices, weakened further in January, fuelling fears that the ECB’s bond-buying programme may not be enough to stave off a downward spiral in prices.

The figures, an early “flash” estimate from the European statistics office, showed core inflation, which excludes the effect of volatile items such as food, alcohol and tobacco, edging down to 0.5% this month from 0.7% in December.

“Today’s inflation numbers fully vindicate the ECB’s decision to embark on QE. That said, QE will not raise inflation in the coming months. Unless oil prices stage a quick recovery, the energy component will keep headline inflation well below zero in the months ahead. But the key number to watch in the coming months is core inflation. Any further falls may raise concerns that QE has come too late to stave off deflation,” said Teunis Brosens at ING Financial Markets.

The ECB aims to keep inflation at just under 2% and Draghi has said the money-printing programme would continue “until we see a sustained adjustment in the path of inflation”.

Separate numbers showed a marginal improvement in the eurozone labour market in December, with unemployment edging down to 11.4%, defying economists’ expectations for it to hold at November’s 11.5% rate. It was the lowest since August 2012.

Timo del Carpio, European economist at RBC Capital Markets, said the unexpected drop in unemployment “serves to tentatively end a period of stagnation that had persisted for the latter half of 2014”.

But he also highlighted that much of the improvement reflected a sharp drop in typically volatile Italian data. “Moreover, while survey indicators of hiring intentions have been improving, they still point to only tepid job creation over the first half of 2015,” he added.

The statistics office, Eurostat, said unemployment was lowest in Germany (4.8%) and Austria (4.9%), and highest in Greece (25.8% in the most recently available figures, from October 2014) and Spain (23.7%).

• This article has been amended after a correction to official figures was issued by Eurostat. Estimated core inflation – the rate excluding energy, food, alcohol and tobacco – was 0.6% in January, not 0.5%, as previously stated.