The Mexican president sent a letter to Spanish King Felipe VI and Pope Francis urging him to apologize for human rights abuses committed during the conquest of the region.
Andrés Manuel López Obrador said the indigenous peoples of Mexico had been victims of massacres.
In a video filmed in the ruins of an ancient Mexican city, he called for a comprehensive account of the abuses.
"The time has come to reconcile, but first ask forgiveness," he said.
"The sword and the cross"
"There was massacre and oppression, the so-called conquest was led by the sword and the cross," he said.
"They built their churches on the (indigenous) temples."
Mexico has the second largest Roman Catholic population in the world after Brazil.
The Madrid government reacted swiftly and resolutely rejected his request for apology.
"The arrival of the Spaniards 500 years ago to present Mexican territory can not be judged by current considerations," Spain said in a statement.
"Our two brother nations have always known how to read our shared past without rage and with a constructive outlook," she added.
The Aztec empire defeats
expedition under the leadership of Christopher Columbus in 1492.
The conquest of Mexico began in 1519 when a small army led by Hernán Cortés landed in what is today the state of Veracruz, years of Spanish rule.
Mexico gained independence after a war that lasted from 1810 to 1821 and became Federal in 1824.
Mr. López Obrador came to power in December with a left-wing agenda.
He promised to tackle corruption reduce inequality and eliminate millions of Mexicans from poverty.
Relations with Spain's center-left government have been friendly so far.