By Hugh Bronstein

UNITED NATIONS (Reuters) - Efforts to stop immigration and the mix of cultures are bound to fail, Mexico's President Enrique Pena Nieto told a United Nations summit on migrants and refugees on Monday, as his country's northern border has become an issue in the U.S. presidential election campaign.

Pena Nieto took a public opinion shellacking for hosting Republican Party candidate Donald Trump on Aug. 31 because Trump has repeatedly vowed to build a border wall to keep out illegal immigrants and said Mexico would pay for it.

"History shows that there are no barriers that can stop either the movement of people or the fusion of cultures," Pena Nieto said in his address to the summit ahead of the U.N. General Assembly.

"Neither natural nor artificial barriers hold sway. For every river there has always been a bridge. For every obstacle there has always been a way forward. Movement is an essential part of human existence," he said.

Trump has infuriated Mexicans with a series of broadsides against the United States' southern neighbor.

"We are a proudly mestizo, multi-cultural and diverse nation," Pena Nieto said, referring to Mexican of mixed descent.

"We Mexicans firmly believe that this mestizo fusion is the future and destiny of human kind."

Hillary Clinton, the Democratic Party candidate in the Nov. 8 election, has accused Trump of embracing a brand of U.S. political conservatism associated with white nationalism and nativism.

She has linked Trump's statements about immigration and religion to the rise of a political fringe movement in the U.S. known as the "alternative right", which opposes multiculturalism and immigration.

(Reporting by Hugh Bronstein; editing by Grant McCool)