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MEXICO CITY, Feb 21 (Reuters) - Mexican central bank chief Agustin Carstens will delay his exit from the institution, the bank said on Tuesday, in a sign of support for the government as it faces tough economic talks with the United States.

The announcement comes amid the country's mounting inflation and the prospect of an economic slowdown due to worries that new U.S. President Donald Trump will impose barriers on U.S.-bound Mexican exports.

Carstens had said on Dec. 1 he would resign from his post at the end of June, to lead the Bank of International Settlements, more than four years before the end of his second six-year term. His announcement had sparked criticism he was leaving at a bad time for Mexico.

But the Swiss-based BIS on Tuesday it had agreed to delay Carstens' start date as its new head, confirming reports from Mexico on Monday.

Carstens, who has led the central bank since 2010, agreed to seek the delay during a recent meeting on Mexico's economic outlook with President Enrique Pena Nieto and Finance Minister Jose Antonio Meade, the central bank said in a statement.

In an interview with Reuters on Monday, Deputy Governor Alejandro Diaz de Leon would not comment on reports of Carstens' decision, but he said the bank faced an "especially complex environment," without precedent, citing rising inflation and weak growth.

Mexico's peso sank to a record low following the November election of Trump, who has threatened to slap tariffs on Mexican-made goods and renegotiate the North American Free Trade Agreement among the United States, Mexico and Canada.

A gasoline price hike has driven inflation to a more than 4-year high, and the economy is expected to slump this year due to the uncertainty of how Trump's policies could affect Mexico's exports and investment in Latin America's No. 2 economy.

Pena Nieto's popularity has been hit by rising crime, rampant corruption and protests about the gasoline price hike.

(Reporting by Michael O'Boyle Editing by W Simon)