* Dlr index pulls back from 2-wk low as Cohn exit shock peters out
* Dollar/yen retraces losses as broader risk appetite recovers
* Euro awaits ECB policy decision for cues
* ECB seen standing pat, stance amid US political confusion eyed (Adds details and quotes, updates prices)
TOKYO, March 8 (Reuters) - The dollar recovered ground on Thursday, drawing relief from positive labour market data and the White House saying Canada and Mexico, and possibly other countries, may be exempted from planned U.S. import tariffs on steel and aluminium.
Elsewhere on the currency markets, the euro trod water ahead of a European Central Bank meeting, later in the day, that is expected to leave policy rates unchanged for now, but may provide clues to the future.
The dollar had weakened sharply following the resignation on Tuesday of Gary Cohn, the top economic advisor to the White House who was seen as seen as a bulwark against protectionism in President Donald Trump's administration.
His departure had fanned fears of a potential global trade war if Trump pressed ahead with proposals for tariffs on all imports of steel and aluminium.
Broader financial markets grew calmer, with Wall Street paring losses overnight, after the White House raised the possibility of exemptions. Some dealers have bet on the possibility that the tariff threat was a negotiating ploy in trade talks with neighbours.
Trump plans to offer Canada and Mexico a 30-day exemption from planned tariffs on steel and aluminum imports, which could be extended based on progress in talks on amending the North American Free Trade Agreement (NAFTA), a White House official said on Wednesday night.
The dollar's recovery was stoked by Wednesday's data on U.S. private hiring and labour costs that reinforced the view of underlying strength in the economy.
The U.S. currency was steady at 106.040 yen after slipping to as low as 105.450 the previous day in reaction to Cohn's departure.
The dollar index against a basket of six major currencies was effectively flat at 89.585 after pulling away from a two-week trough of 89.407 the previous day.
"The market has managed to digest Cohn's resignation," said Junichi Ishikawa, senior FX strategist at IG Securities in Tokyo. "That said, 'Trump risk,' which are developments associated with the U.S. president and his circle, will continue to impact the market as one of the main themes of 2018."
While worries about U.S. tariffs may have eased somewhat, the dollar's recovery was limited as fears of trade conflicts lingered with Trump seen sticking to a protectionist stance in the longer run.
Daisuke Karakama, chief market economist at Mizuho Bank in Tokyo, said that while the currency market is difficult to predict, the dollar "will almost certainly weaken" if that's what the United States wants to happen.
"Along with tariffs, weakening your own currency becomes a weapon in a trade war," he said.
The euro was little changed at $1.2408 after retracing a bounce earlier on Wednesday to a 2-1/2-week peak of $1.2447.
Focus for the common currency was on the ECB's policy decision at 1245 GMT. The central bank is all but certain to keep policy unchanged but may tweak its communication stance to offer at least a few clues about its progress towards ending its unprecedented bond purchases later this year.
"Under normal circumstances the ECB decision would not be a risk event as the central bank is expected to stand pat on policy. But the ECB's stance will be watched carefully in the wake of political confusion in the United States," Ishikawa at IG Securities said.
The Canadian dollar was 0.2 percent firmer at C$1.2881 per dollar, having weakened to C$1.3002 on Wednesday but recovering on the prospect that Trump's tariffs may exempt Canada and Mexico.
The Mexican currency was at 18.68 pesos per dollar following its recovery from 18.90 touched on Wednesday.
The Australian and New Zealand dollars were 0.1 percent higher at $0.7833 and $0.7292, respectively. (Editing by Simon Cameron-Moore and Richard Borsuk)