TMZ Sports has obtained video that shows Conor McGregor taking his rape accuser by the hand and leading her into a bathroom ... where she says he sexually assaulted her.

The footage was shot inside the Kaseya Center in Miami at around midnight on June 10 ... just after the Nuggets had beaten the Heat in Game 4 of the NBA Finals on June 9.

In the video, you can see McGregor -- wearing a black tee -- leaving a restroom area to speak with a woman in a white shirt. After appearing to exchange words with the woman, Conor grabs her by her hand and makes a path for her to go with him inside of a bathroom.

A few seconds later -- the restroom door shuts, without anyone else appearing to go inside. The footage then ends.

TMZ Sports broke the story ... earlier this week the accuser's lawyer, Ariel Mitchell, sent a demand letter claiming NBA and Miami Heat security "physically forced" the accuser into the restroom, where McGregor proceeded to rape her while security refused to let her exit or allow her friend to come into the bathroom with her.

However, the video does not appear to show anyone forcing her into the restroom with Conor (he is instead leading her by the hand), but three men who seem like security guards do assemble in front of the door in a manner that would prevent anyone from entering or exiting.

According to Mitchell ... McGregor's accuser and the UFC star had been partying together at a club inside of the NBA arena just minutes before our video was taken.

At one point during their nightclub celebration, Mitchell tells us her client took a selfie video with Conor.

Mitchell says, though, their partying was halted when McGregor said he had to use the restroom -- but shortly after he got up, a man in a Denver Nuggets jersey walked up to her and told her, "Conor told me to come get you."

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