Mr Lopez Obrador said he sent a letter to King Felipe VI of Spain and Pope Francis over what he called an "invasion" and the "many misdeeds that were committed".
"There were killings, impositions," the president said in a video that was filmed at Mayan ruins in the south-eastern state of Tabasco and posted on social media.
"The so-called conquest was carried out with the sword and the cross."
He asked for an apology to "the original peoples for the violations of what are now known to be human rights".
The Spanish government issued a statement later regretting that the 1st March letter had been made public and rejecting its content "with all firmness".
"The arrival, 500 years ago, of Spaniards to what is today Mexican territory cannot be judged in the light of contemporary considerations," it continued.
"Our sibling peoples have always known how to read our shared past without anger and with a constructive perspective, as free peoples with a common inheritance and an extraordinary projection."
The statement reiterated the Spanish government's willingness to work closely with Mexico to strengthen friendly and co-operative relations and tackle future challenges.
The exact text of the letter has not been made public.
Mr Lopez Obrador called for 2021 - the 500-year anniversary of the conquest of Tenochtitlan, the capital of the Aztec empire on what is today Mexico City - to be a year of "historic reconciliation".
Spain's President Pedro Sánchez
"It is time to say we will reconcile but first let us apologise," he said. "I am going to as well because after the colonisation there was much repression of the original peoples."
In 2015, Pope Francis apologised in Bolivia for crimes of the Roman Catholic Church against indigenous people during the conquest of the Americas.
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