* Euro back above $1.3600 after ECB action
* U.S. non-farm payrolls set to dominate trade
* Dealers see any euro rise capped below $1.37 (New throughout, changes dateline from previous SYDNEY/SINGAPORE)
By Patrick Graham
LONDON, June 6 (Reuters) - The euro held on to gains against the dollar on Friday, a day after investors covered bets against the single currency in response to long-promised steps by the European Central Bank to bolster growth.
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.
But investors preferred to take profit on two weeks of falls than push the single currency lower, putting put it firmly back in a range it has held since December.
Many dealers and strategists said the ECB had not done enough to weaken the euro. Several said U.S. jobs data on Friday would only add to pressure on the dollar, trading at its lowest in a week against a basket of currencies.
"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 will depend on the U.S. data getting stronger."
The euro last traded at $1.3645, having recovered from a trough of $1.3503 set on Thursday shortly after the ECB's policy announcement.
Dealers said many players who had been short of euros into the ECB meeting - effectively betting on further losses - had been squeezed by the bounce afterwards. But they said there were substantial sell orders for the euro around $1.3680-1.3690, likely to cap any further gains.
Jeffrey Halley, an FX trader for Saxo Capital Markets in Singapore, said the initial drop on Thursday may have set an interim low for the euro that could hold over the next few weeks.
Asked for his stance on the euro, he said: "It's buy dips to $1.3600 looking for a squeeze to $1.3800."
One of the big trends to have supported the currency this year still looked firmly in place on Friday - investors pushing more money into the euro zone's peripheral southern bond markets, where yields are still a little higher than those in the U.S. and Germany.
Still, some analysts believe the euro could resume its downtrend fairly quickly. Analysts at BNP Paribas recommended selling the euro at $1.3620 to target a move to 1.3200, with a stop at $1.3820.
"EURUSD has squeezed higher after the announcement but we think this is an opportunity to add to shorts," they said.
The rebound in the euro weighed on the dollar index, which measures the greenback's value against a basket of major currencies. The dollar index last stood at 80.311, down from Thursday's four-month peak of 81.020.
Against the yen, the dollar eased 0.2 percent to about 102.24 yen.
Analysts polled by Reuters expect U.S. employers probably added 218,000 jobs in May, a step down from April's gain of 288,000. But estimates are even wider than usual, ranging from 110,000 all the way to 325,000.
(Editing by John Stonestreet)