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The video, which is reportedly from 2015, is the second video showing a brother of the president accepting large amounts of cash.
The footage was filmed just ahead of a national vote in which the now-ruling Morena party was competing in its first election.
In the video released late on Thursday by Mexican news outlet Latinus, Martin Jesus Lopez Obrador can be seen receiving an envelope stuffed with a large stack of bills, which a narrator says totalled 150,000 pesos (£5,452) and were part of a recurring set of payments.
Latinus claimed that if the cash was not reported by Morena to the electoral authorities, it could constitute an “electoral crime”
The man in the video giving the president’s younger brother was identified as David Leon, a political operative who served as an adviser to Mr Lopez Obrador before heading Mexico’s civil protection agency. He gave up the government job last August.
Hours after the video was released, Mr Leon posted on his personal Twitter account stating that the bundles of cash “were in a personal capacity, product of my savings and on the occasion of a loan,” Latinus reported.
In response to the video, the president said: “I think the intention is to do damage to me, or to try to damage me.
“It’s the perennial black campaign of my adversaries. We’re used to this. But we have always emerged unscathed from slander.”
He said he would not cover up for anyone, and that authorities should investigate whether any crime had been committed, and punish any wrongdoing.
“But my conscience is clear,” added Mr Lopez Obrador, who has built his reputation as an indefatigable scourge of corruption.
Additional reporting by Reuters