Carrie Ann Inaba and Val Chmerkovskiy Have 'Cathartic' Conversation, Hug It Out

Carrie Ann Inaba and Val Chmerkovskiy have buried the hatchet ... after the pro dancer made an off-color joke about Will Smith's infamous Oscars incident that made Carrie Ann feel threatened and led to his brief suspension.

Carrie Ann told Val after Tuesday's "Dancing With the Stars" episode, in a video obtained by PEOPLE, "So, everyone's staring. We are coworkers, and we are completely cordial. We are good, OK?"

After the reconciliation -- which saw the co-stars hugging it out -- Val told the publication ... "It felt [like] cathartic relief, you know? I think it was just really important for me to make sure that she feels safe and knows that, firsthand from me, I want nothing but love for her."

Sources close to the show tell TMZ ... Val approached Carrie Ann and told her he wanted to put this behind them and make sure they both felt OK after a tumultuous few weeks. We're told Carrie Ann was very gracious and their conversation was uplifting for everyone on set.

We reported earlier ... Val was all smiles last week after he returned to rehearsal following his 1-episode suspension.

As you know ... Val caused quite a stir after seemingly implying he wanted to slap Carrie over her criticism of his wife Jenna Johnson and dance partner Harry Shum Jr.'s performance.

Val wrote in a since-deleted TikTok comment ... "You almost saw the Fresh Prince enter the ballroom last night" ... and later apologized.

As a result ... sources told us that Carrie brought it up with BBC Productions and claimed she felt threatened by the comment.

After an investigation into the remark ... Val was suspended for an episode.