In a short clip posted on social media from Uruguayan TV programme Por La Camiseta, host Rafa Cotelo asked Bentancur for a Spurs player's shirt, to which he replied: "Sonny's? It could be Sonny's cousin too as they all look the same."
The midfielder apologised for his comments last week.
"I've spoken with Lolo (Bentancur)," South Korea captain Son said in a post on Instagram.
"He made a mistake, he knows this and has apologised. Lolo would not mean to ever intentionally say something offensive. We are brothers and nothing has changed at all.
"We're past this, we're united, and we will be back together in pre-season to fight for our club as one."
In a separate statement on Thursday, Spurs said they would provide further education to all players "in line with our diversity, equality and inclusion objectives".
"We fully support that our captain Sonny feels that he can draw a line under the incident and that the team can focus on the new season ahead," the Premier League club added.
