* Euro regains footing, Italy's vote result seen as expected
* But Italian politics still seen as a focal point
* Dollar index steady, nurses previous day's losses
SINGAPORE, Dec 6 (Reuters) - The euro steadied on Tuesday, having bounced back from a near 21-month low set the previous day after Italian Prime Minister Matteo Renzi's loss in a referendum over constitutional reform, an outcome that traders had widely expected.
Renzi announced on Monday that he would resign after the resounding defeat. The size of the "No" vote at 59.1 percent, was more emphatic than many had forecast. resignation could open the door to an early election next year and the possibility of the anti-euro 5-Star Movement gaining power, though many investors and analysts see it as more likely that a caretaker government will be put in place until an election in 2018.
The euro eased 0.1 percent to $1.0751 EUR= but held on to the bulk of the gains from Monday, when it ended up gaining about 1 percent on the day, bouncing from a low of $1.0505 set after Renzi said he would resign.
The euro's bounce partly reflected the fact that the market had been expecting a "No" vote in the Italian referendum, said Steven Dooley, currency strategist for Western Union Business Solutions in Melbourne.
"There had been some fears of a worst case scenario, seeing the president of Italy call for an immediate election... and because that doesn't seem to be occurring in the near term, that's another reason why some of the heat is taken out of this trade," Dooley said.
Analysts said political developments in Italy would remain a focal point for the euro, although it may have gained some respite for now.
"If it weren't for yesterday's rally, I would have said that it would be hard to buy the euro because uncertainties would linger," said Masafumi Yamamoto, chief currency strategist for Mizuho Securities in Tokyo.
"But after seeing that rally yesterday and given that Renzi seems likely to stay on, at least for this week, there may be a lack of reasons to sell the euro in the near term," Yamamoto said.
The dollar held near a three-week low against a basket of six major currencies as investors viewed recent strength as overdone.
The dollar index last traded at 100.17 .DXY . On Monday it had slipped to as low as 99.849, its lowest level since Nov. 15.
The index had set a 13-1/2 year high of 102.05 in late November, having rallied as U.S. bond yields surged on expectations of higher fiscal spending and a faster pace of Federal Reserve monetary tightening under President-elect Donald Trump.
Against the yen JPY= , the dollar slipped 0.3 percent to 113.55 yen.