* German HICP inflation at 1.1 pct (forecast 1.3 pct)
* Euro zone data due on Weds, expected to show pickup
* German data heightens dilemma for ECB
(Adds detail, quotes)
BERLIN, April 29 (Reuters) - German annual inflation accelerated in April but less than expect, preliminary data showed on Tuesday, complicating the European Central Bank's decision on whether to act against deflationary trends.
Euro zone inflation is running at 0.5 percent and there are concerns about deflation. A report due on Wednesday is expected to show inflation in the euro bloc picking up to 0.8 percent in April, but that would still be well below the ECB's medium-term target of just below 2 percent.
On Monday ECB President Mario Draghi played down the likelihood of any imminent money-printing to buy assets, saying that while low inflation would persist, such quantitative easing remained a way off, according to a source.
German consumer prices harmonised to compare with other European Union countries - the HICP measure of inflation used by the European Central Bank - rose by 1.1 percent in April, data from the statistics office showed.
That was less than the 1.3 percent forecast in a Reuters poll although it compared with 0.9 percent in March.
"The increase is slightly too small to really lean back and relax... It's clearly going to give them a headache," said ING senior economist Carsten Brzeski.
"If the increase in euro zone inflation tomorrow is also only as small as the German HICP increase, the chances of action have increased, combined with today's disappointing monetary data," he added.
Other data on Tuesday showed lending to euro zone households and companies declined further in March and money supply growth slowed.
Christian Schulz, senior economist at Berenberg bank, said the German inflation reading could point to a lower-than-forecast euro zone figure and could therefore pile more pressure on the ECB to ease policy soon.
Although ECB staff forecasts in March pointed to inflation picking up to 1.5 percent in 2016, and 1.7 percent in the final quarter of that year, the central bank has faced pressure to act - in particular from the International Monetary Fund.
"I think that monetary policy should do everything it can in order to make sure that inflation goes back to fulfil the mandate of the ECB," Jose Vinals, director of the IMF's monetary and capital markets department, told Reuters on Monday.
Last week, Draghi set out three scenarios under which the bank could act: an unwarranted tightening of the policy stance, impairments in the transmission of policy, or a deterioration of the medium-term inflation outlook.
ECB Vice President Vitor Constancio said on Monday April's inflation figures for the euro zone should not alone trigger a policy change because "it's not just one or two numbers that matter".
Moderate inflation, combined with a strong labour market and low interest rates, is helping to boost domestic demand, on which the government is relying to prop up growth this year as foreign trade is expected to be weak.
A survey by GfK market research group published on Tuesday showed German consumer morale remained at its highest level in more than seven years heading into May as consumers' income expectations hit a record high, helped by modest inflation and expectations that pay will rise.
But Schulz said German inflation was likely to pick up.
"There's real hope that German inflation will stabilise and gradually increase due to domestic pressures such as wage settlements, which could be quite generous given the very low unemployment rate in Germany and the strengthening recovery," Schulz said.
Unions have already secured strong wage hikes for chemical workers and public sector employees this year and GfK market research group has said the first wage deals in 2014 suggested that wage increases of 3 percent or more were realistic.
(Reporting by Michelle Martin; additional reporting by Paul Carrel in Frankfurt; Editing by Jeremy Gaunt/Madeline Chambers)