"I am prepared to apologise. This was not a good publication," Anki Ahlsten, who is also the party secretary, told newspaper Expressen on Wednesday.
The unofficial tell-all biography "Carl XVI Gustaf - the reluctant monarch" ("Carl XVI Gustaf - Den motvillige monarken") went on sale on November 4th.
Sweden's Royal Court has accepted the apology, but its lawyer will continue to review the publication to determine whether to file a possible lawsuit.
Royal Court communications director Bertil Ternert told The Local on Tuesday that a course of action has not yet been decided upon.
"We don't know what actions we will take. We will wait and see what our lawyer's opinion is. We will hear from him in a couple of days. I can't comment on any details about it," he said.
"I can only say that we think our lawyer has to look at it. It has nothing to do with the book. There is no connection to that. The author of the book, he also told readers there is nothing in the book about this," said Ternert.
According to Expressen, Vänsterpress wrote in the book review, "And the Swedish people pay for the feasts, both weddings, parties and whores."
The biography on the King chronicled details of wild parties and affairs he had with young women. It is the first book of its kind in Sweden.
One of the most controversial revelations was an alleged year-long affair with Swedish singer and model Camilla Henemark, born to a Nigerian father and a founding member of the band Army of Lovers.
The King's daughter, Princess Madeleine, won libel damages worth over 3.5 million kronor ($540,000) last week from a number of German newspapers for intruding in her private life. The stories reported false allegations and claims about her life and lifestyle habits from 2000 to 2004.
The princess broke off her engagement to lawyer Jonas Bergström weeks before her sister Crown Princess Victoria's wedding to Prince Daniel in June 2010 after a Norwegian handball player reported an encounter with him. The princess is now based in New York.
The Local has made several unsuccessful attempts to contact the Royal Court for further comment on Wednesday.