TMZ reported the pair separated last week due to Odom's alleged cheating and addiction to crack cocaine, but the celebrity news website said neither Kardashian nor Odom has consulted a lawyer or filed divorce papers.
"Really hard to sit here and listen to people talk [expletive] about my family!" Kardashian tweeted Sunday. "[Expletive] you and shame on you! I'm too protective for this [expletive!]"
Kardashian had not previously addressed gossip regarding the supposed breakup of her marriage, but she tweeted the messages, "Stop trying to figure me out and get to know your self first" and "Only the strong will survive" on Aug. 21 and 23, respectively.
Kardashian and Odom married in 2009 after a four-week courtship.