TMZ spoke with Hilton ... who tells us, "I apologize to Lindsay for the comment that I made. I was joking around but it was thoughtless and unnecessary."
We broke the story ... Hilton zinged Lohan on her reality show, "The World According to Paris" -- taking a shot at Lohan about her theft case. Lohan told friends she was hurt by the comment.
But Hilton insists she's serious about repairing the relationship ... saying, "I am reaching out to Lindsay so I can tell her myself."