"It is looking an ever closer call on whether the ECB will take further measures, and it is very possible that the bank could act as soon as its April 3 policy meeting," said IHS Chief Economist Howard Archer.
Prices are now falling in five eurozone countries. But ECB President Mario Draghi and other officials have said they see no evidence of deflation across the region as a whole.
Still, they have warned of the risks of an extended period of low inflation and have said that the strength of the euro at around $1.40 is contributing to pressure on prices.
The March number was depressed by slowing food price inflation, and a big fall in energy costs, both factors over which the ECB has little control -- and the bank is likely to pay greater attention to the strength of the currency, Archer said.
A late Easter holiday this year -- in April rather than March -- may also have had a dampening effect as retailers and travel operators wait for next month to introduce seasonal price increases.
A slide into deflation could depress economic activity still further as spending is postponed in anticipation of lower prices. It would also raise the real value of the debt already weighing down on many eurozone countries.