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"I probably have a very good relationship with Kim Jong- Un," Trump was quoted as telling The Wall Street Journal in an interview on Thursday, refusing to confirm whether the two had spoken.
"President Trump said, I'D probably have a very good relationship with Kim Jong Un of North Korea. I'D -- I'D -- I'D. NOT I!" the message read, with "I'D" in red ink, under a red banner reading "FAKE NEWS."
Mockingly mimicking the newspaper's front page, it then reads "THE WALL STREET JOURNAL -- FAKE NEWS IS AT IT AGAIN! -- FALSELY QUOTING PRESIDENT TRUMP."
Washington and Pyongyang are in a standoff over North Korea's missile and nuclear programs, which could be used to target the United States and its allies.
Trump has repeatedly insulted the North Korean leader, describing him as mad and a "rocket man."
Asked if he had spoken to Kim, Trump said "I don't want to comment on it. I'm not saying I have or haven't. I just don't want to comment."
Trump suggested his variable position on individuals was part of a broader strategy.
But it was not clear how his remarks fit with his self- described policy of "maximum pressure" on Pyongyang.