UPDATE 1-Mexico's Carstens says inflation to ease in 3rd qtr-BBG

(Adds quotes, details, background)

MEXICO CITY, July 5 (Reuters) - Mexican inflation is likely to come back below the central bank's 4 percent ceiling during the third quarter, central bank Governor Agustin Carstens was quoted on Thursday as saying.

The Banco de Mexico aims for inflation of 3 percent, but has a tolerance band of one percentage point either side. Inflation jumped to a 1-1/2 year high of 4.3 percent in early June.

"During this quarter it is very likely that inflation will come back to our range," Carstens said in an interview with news agency Bloomberg, according to a report posted on its website.

The Banco de Mexico has held interest rates at 4.5 percent since mid-2009, in the midst of a deep recession, and at its last meeting dropped an earlier flirtation with interest rate cuts to move to a neutral stance.

"We believe that a neutral stance is adequate," Carstens was quoted as saying, citing strong domestic growth coupled with international volatility.

Mexico's peso slumped to a three-year low at the beginning of June. It has recovered about 9 percent since then, but it is still trading around 13.34 per dollar and Mexican policymakers have worried that the weak peso could fan inflation since it blew past 12 per dollar last year.

The peso is one of the most liquid emerging market currencies in the world, making it a favorite instrument for speculators who make bets based on the general global appetite for riskier assets.

But policymakers are unlikely to worry about high inflation fueled by seasonal factors. So far, there has been only a slight impact on core goods prices due to the peso weakness.

Bloomberg reported that Carstens said an improvement in the United States and Europe could help push the currency to near 12 per dollar.

"I wouldn't be surprised if certain scenarios present themselves, we could see exchange rates close to that level," he was quoted as saying. "Given that we have no structural problems in the financial system, you would think the peso has room to appreciate."

Mexico's economy expanded strongly in the first quarter, although more recent data have been mixed. Carstens was reported as saying he thought growth in Latin America's second-largest economy this year would probably be between 3.5 percent and 4 percent and it was less likely to near the top of the central bank's forecast range of 4.25 percent.

(Reporting by Krista Hughes; Additional reporting by Michael O'Boyle; Editing by Leslie Gevirtz)