MEXICO CITY, July 31 (Reuters) - Mexico's peso pared gains to trade nearly flat on Friday 31 July after key U.S. economic data showed consumer spending in the United States shrank in the second quarter, pointing to a sluggish recovery for Mexico's exports.

The peso MXN=MEX01 cut gains to trade at 13.244 per dollar, still 0.05 percent firmer from Thursday (30 July)'s close.

The U.S. economy contracted at a slower-than-expected pace in the second quarter, backing views the recession there is winding down.

But the report showed consumer spending, which accounts for more than two-thirds of U.S. economic activity, fell at a 1.2 percent rate in the second quarter after rising 0.6 percent in the previous quarter.

The U.S. downturn has pushed Mexico into its deepest recession since the Great Depression of the 1930s, and a sluggish recovery in consumer spending will damp down a rebound in Mexican exports, 80 percent of which are sent to the United States.

Earlier in the session, the peso made gains to just below the 13.20 level. Its initial retreat after the U.S. data took it to 13.25, but it bounced back, setting a clear range that has been evident since last week.

"A lack of conviction with regards to investing in Mexico is likely to prolong this range-bound trading, and see the peso continue to underperform any region currency strength," HSBC strategist Clyde Wardle wrote in a report to clients.

Mexico's peso has lagged the gains of other emerging market peers amid uncertainty about how quickly a U.S. recovery could help local exports rebound and concerns Mexico faces a debt downgrade as the country's fiscal accounts weaken.

(Reporting by Michael O'Boyle; Editing by Kenneth Barry)