SINGAPORE, June 5 (Reuters) - The dollar steadied on Wednesday, ahead of a policy meeting in Canada that traders have bet will begin the cutting cycle for some of the world's biggest economies.

The Bank of Canada meets a day ahead of a European Central Bank meeting on Thursday. Markets price about a 75% chance of a Canadian rate cut and a 95% chance of a cut in Europe.

The Canadian dollar hugged the middle of a months-long range at C$1.3678 per dollar - as did the euro at$1.0881 - and at both meetings the outlook will be in focus at least as much as the decision.

"If they suggest there's a green light to a lot more cuts this year, then I think that could really weaken the Canadian dollar," said Commonwealth Bank of Australia strategist Joe Capurso.

The yen slipped about 0.4% to 155.56 per dollar in an otherwise quiet Asia, retracing some of an overnight gain that was driven by investors unwinding bets in emerging markets.

Japanese real wages fell for a 25th straight month in April, data on Wednesday showed, as inflation outpaces nominal pay rises. The yen is the worst-performing G10 currency this year, by some margin, and on Tuesday BOJ Deputy Governor Ryozo Himino said the central bank must be "very vigilant" to the impact the currency's weakness could have on the economy and inflation.

The Australian dollar he Australian and New Zealand dollars edged up after domestic economic news proved less dire than investors had feared.

A reading on the Australian economy showed it grew just 0.1% in the first quarter, as interest rates and elevated inflation squeezed consumer spending. Markets, however, had been braced for contraction, so even that tiny gain was enough to prompt short covering and the Aussie was last up 0.1% to $0.6657.

The New Zealand dollar rose 0.1% to $0.6184 and sterling was steady at $1.2775.

Emerging markets, meanwhile, stabilised after a turbulent few days.

India's rupee recovered from the seven-week low it hit in a wild session for Indian markets as election results showed voters had returned Narendra Modi on a much slimmer margin than had been expected.

South Africa's rand has wobbled after the African National Congress lost its parliamentary majority for the first time in 30 years.

And the Mexican peso steadied after dropping some 4% on the dollar and nearly 6% on the yen since the ruling left-wing Morena party was re-elected and, in coalition, within reach of two-thirds majorities in both Congress chambers.

Heavy selling of the peso against the yen showed investors pulling back on one of the most popular "carry" or interest-earning trades, said Pepperstone's head of research Chris Weston, as the outlook for Mexico's currency is uncertain.

"The trigger ... has been the pricing that the Morena party’s majority in Congress (means a) mandate to push forward with major structural reforms and see greater government control over businesses and the economy – a factor that potentially reduces Mexico’s standing as an international hub."

(Reporting by Tom Westbrook; Editing by Lincoln Feast)