The former child star's representative told E! News last week the story is "not only categorically without merit, but it is also impossibly and ridiculously fictitious."
"We beseech the responsible media to consider the source and its reputation, and to please not perpetuate this destructive and insulting story by pursuing it any further," the actor's publicist said.
However, the tabloid newspaper said it refuses to retract or amend its report.
"The National Enquirer hopes the cover story on its latest issue, "'Home Alone' star Macaulay Culkin Addicted to Heroin -- Only 6 Months to Live!" will act as a dramatic and much-needed wake-up call to the 31-year-old actor," the tabloid's representatives said in a statement posted on its Web site.
"Our advice to Macaulay is to seek professional help to avoid the same tragic fate of other beloved celebrities, including Whitney Houston, who died earlier this year," the statement goes on.
"We believe that the former child star should be doing everything he can to get the treatment he so desperately needs -- and which could have saved the life of his friend Elijah Rosello. Her family confirmed to The Enquirer that she did drugs with Macaulay before her drug-related death in March.
"Should Macaulay's representatives continue to deny The Enquirer's accurate and detailed report, we are ready to offer him the opportunity to take a blood test administered by an independent medical lab. It is a fact that as The Enquirer tracked Whitney Houston's descent into her drug hell, she refused to admit she had a problem -- and Whitney was represented by some of those people now denying Macaulay's potentially deadly problems.
"The Enquirer editors would hate to see Macaulay end up like Whitney."
Culkin was a famous child star of the 1980s and '90s, appearing in the blockbuster "Home Alone" comedies, as well as the films "Uncle Buck," "My Girl" and "The Good Son." As an adult, he has co-starred in several independent movies and worked as a disc jockey.
Notable deaths of 2014 [PHOTOS]