* Mersch says sees no signs of deflation in euro zone
* Very low inflation for too long bears risks
* Weidmann says low inflation to last for some time
* ECB will watch euro moves closely -Weidmann
* Nowotny - negative deposit rate "discussed intensively" (Adds Nowotny comments, FAZ on deposit rate)
FRANKFURT/VIENNA, May 19 (Reuters) - There were increasing signs on Monday that the European Central Bank will add more stimulus to the euro zone economy at its June policy meeting as inflation remains stuck at very low levels.
ECB Executive Board member Yves Mersch said the likelihood of policy action at the bank's next meeting had grown substantially, warning about the risks of inflation staying very low for too long, even though there were no signs of deflation.
President Mario Draghi said after the ECB's May meeting that the Governing Council was "comfortable with acting next time" - its June 5 policy meeting - but wanted to see updated economic projections from the bank's staff first.
Since then, data has confirmed a slight increase in euro zone inflation in April to 0.7 percent, from 0.5 percent the previous month, but also shown that the economy grew much less than expected at the start of the year.
"The likelihood that the Governing Council will already act at its next monetary policy meeting in June has grown substantially," Mersch said in the text of a speech for delivery in Munich.
He said the Governing Council was unanimous in its willingness to deploy both conventional and unconventional measures to effectively counter the risks of very low inflation over a longer period of time.
A too-long period of very low inflation risked unanchoring long-term inflation expectations, Mersch said. He described various deflationary risks, adding: "We see no sign at the moment that such a deflationary scenario will materialise in the euro zone."
In Vienna, another ECB policymaker, Ewald Nowotny, echoed Mersch's view that the euro zone was facing a prolonged period of low inflation but not deflation. He also said the exchange rate had an effect on price stability.
Last week, Reuters reported that the ECB was preparing a package of policy options for the June meeting, including cuts in all its interest rates and targeted measures aimed at boosting lending to small- and mid-sized firms.
One policy option under discussion is for the ECB to cut into negative territory the deposit rate it pays banks for holding their cash overnight - a move that would see it effectively charge them for parking money at the central bank.
"If one goes very deep with the main refinancing rate, the deposit rate can go into negative territory," said Nowotny, Austria's central bank chief. The main refinancing rate is currently at 0.25 percent.
"This is a point that is being discussed very intensively now," Nowotny added. "The European Central Bank would be the first and only central bank in the world that would have a negative deposit rate."
Separately, the Frankfurter Allgemeine Zeitung, a respected German newspaper, reported that there were concerns on the ECB's Executive Board - the nucleus of the broader policymaking Governing Council - about a negative deposit rate.
"The negative rate has some unintentional, negative side effects," the paper quoted a board member as saying.
Jens Weidmann, head of the German Bundesbank and who leads the hawkish camp on the ECB Governing Council, said inflation would stay low for some time and policymakers would pay close attention to the euro's exchange rate in this context when taking policy decisions.
But he warned against taking too one-dimensional a view of the euro's strength, stressing the importance of the stimulative effect of lower sovereign bond yields in the euro zone.
Investors' renewed appetite for euro zone sovereign bonds could contribute to an appreciation of the euro but the lower yields should have an expansionary effect on financing over the medium term, Weidmann said in a speech in Frankfurt.
"It would therefore be too short-sighted only to take a one-dimensional view of the exchange rate and to leave out the stimulating effects of lower sovereign bond yields," he said.
Last week, Reuters reported the ECB was preparing a package of policy options for the June meeting, including cuts in all its interest rates and targeted measures aimed at boosting lending to small- and mid-sized firms.
The ECB has faced pressure from the French government to change monetary policy course to weaken the euro, whose strength poses risks to euro zone exports.
Weidmann, referring to demands for the ECB to tackle the euro's exchange rate, said: "In order to strengthen growth and employment in the euro zone over time, member states must deliver competitive economic structures." (Additional reporting by Georgina Prodhan; Writing by Paul Carrel and Eva Taylor; Editing by Alison Williams)