The demands are contained in a letter addressed to the president and published on the Ukrainian Pravda website Tuesday.
On Monday, Yushchenko accused the journalist of having "a biased approach toward his son, Andrei," the letter said.
Commenting on information posted by Leshchenko on the Ukrainian Pravda website, the president said, "He is not a journalist. This is a dirty job."
Yushchenko called the author of an article about his son a "killer who never worked for the freedom of the press."
Journalists shot back at Yushchenko, calling his behavior unacceptable.
"We believe the tone and the wording you chose to answer a question about your son's lifestyle are unworthy of a leader of a democratic European country," the letter said. "We insist that you always respect the journalistic profession and the constitutional right of freedom of speech and free access to information."
