* Euro touch lower but still above $1.3600 after ECB action
* U.S. non-farm payrolls set to dominate trade
* Dealers see any euro rise capped below $1.37 (Adds new prices, quotes)
LONDON, June 6 (Reuters) - The wait for U.S. jobs data becalmed major currency markets on Friday as debate raged on the outlook for the euro after the European Central Bank took long-promised steps to push yet more cash into the economy.
Dealers said interest around options at $1.36 helped drag the euro about a quarter of a percent lower against the dollar, but the single currency was still trading almost 1 percent above lows hit when the ECB cut interest rates into negative territory on Thursday.
Volumes of euro-dollar trading, up to double the past month's average on Thursday, were 30 percent below the daily average.
"What is clear is that it is going to be a real struggle to get the euro any lower," said Jane Foley, a currency strategist with Rabobank in London.
"That will really depend on the dollar bulls re-emerging and that (in turn) will depend on the U.S. data getting stronger."
It may take until next week for the dust to settle on the ECB's moves, making good on hints that it would take strong action to both support the economy and, in passing, halt gains for the euro which have driven inflation close to zero.
A 4 percent rise in the euro between January and the start of May has been one of this year's big surprises on financial markets, shaking out a raft of investors who had bet on the dollar strengthening across the board.
The conclusion of many from Thursday's action is that the ECB on its own will struggle to weaken the single currency.
"It is still all about the Fed," said one London-based dealer. "Until we get more certainty about the prospect of stronger growth and higher interest rates in the United States, there are too many other factors in the euro's favour."
The euro traded 0.2 percent weaker at $1.3628. Dealers said there were options to buy more than 3 billion euros set at $1.3600, naturally dragging the currency towards that number given the lower volumes of trade.
U.S. employers are expected to have added 218,000 jobs in May, down from April's 288,000. But estimates are even wider than usual, ranging from 110,000 to 325,000.
There were still voices in the market casting the ECB's cut of interest rates into negative territory as the game-changer that may shift the torpid mood brought on by universally low rates across the developed world.
Analysts at BNP Paribas recommended selling the euro at $1.3620 to target a move to $1.32, with a stop at $1.3820. "EURUSD has squeezed higher since the announcement but we think this is an opportunity to add to shorts," they said.
The factors that have supported the euro this year remain in place, however. Germany's huge trade surplus keeps exporters' cash flowing back into the euro zone and investors pushed more money into the peripheral bond markets on Friday, anticipating the ECB's move will aid a rally in assets that give even a small premium over U.S. and German bonds.
Dealers said there was still interest in buying the euro from Asian central banks needing to convert the dollars they have bought this year to weaken their own currencies.
The consensus on Friday was that without any stronger impulse from the dollar side, it would take the sort of outright government bond-buying implemented by the U.S. Federal Reserve to undermine the euro.
"Looking at yesterday's price movements, it is clear that Mr Draghi's comment on the low likelihood of any further downward movement in the deposit rate was the catalyst for a brutal squeeze on the speculative community's short positions," said Simon Derrick, chief market strategist at BNY Mellon in London.
"Although we have to wait to see what happens in the run-up to the implementation of the negative depo rate next Wednesday, it seems unlikely the leveraged community will be particularly interested in rebuilding these positions unless the ECB starts openly discussing asset purchases in the near future." (Editing by Catherine Evans)