"What's been harder & more painful is being hurt by someone so close to me. Someone whom I love & treat like a little sister. But Jordyn is not to be blamed for the breakup of my family. This was Tristan's fault."
Kardashian then added: "I have to move on with my life & count my blessings, my family, my health, & my beautiful baby True."
It came a day after Woods broke her silence over the cheating scandal in an interview with Jada Pinkett Smith on "Red Table Talk".
Woods admitted she and Thompson kissed … but didn't have sex at a house party in Los Angeles.
"I'm not thinking, 'I shouldn't be here,'" Woods said. "That's my first step where I went wrong."
She added: "I should have gone home after the party. I shouldn't even have been there."
"Never once was I giving him a lap dance, making out with him, sitting all over him. It's just — we're all together," she said.
"We're in a group. Never once did we leave the public area to go to a bedroom, a bathroom — we're all in plain sight."
Kardashian immediately took to Twitter, accusing Woods of lying.
"Why are you lying @jordynwoods ??," Kardashian tweeted after Woods' interview.
"If you're going to try and save yourself by going public, INSTEAD OF CALLING ME PRIVATELY TO APOLOGIZE FIRST, at least be HONEST about your story.
"BTW, You ARE the reason my family broke up!"
Meantime, Kylie Jenner and Travis Scott are said to still be together amid cheating allegations around their relationship.
Jenner, 21, accused her rapper boyfriend of cheating on her this week but is reportedly not making any moves to break up, according to TMZ.
The Sicko Mode rapper, 26, who shares 1-year-old Stormi with the Kylie Cosmetics makeup mogul, has denied being unfaithful, "Page Six" reports.
Scott had an extreme reaction to the scandal by deleting his Instagram account yesterday, despite using social media to promote his Astroworld Tour and merchandise line.
After a string of internet rumours about Scott's alleged cheating, Jenner was said to have found "evidence" on his phone and Scott then cancelled his show in Buffalo, New York, to be with her.
The "Astroworld" rapper — who has denied the infidelity claims — is due to perform at Madison Square Garden in New York today.