Meredith McIver apologized in a statement sent out by the campaign and said Donald and Melania Trump did not accept her resignation.
The statement comes more than 36 hours after reporters uncovered striking similarities between the two speeches --during which time the controversy cast a shadow over Trump's nominating convention and distracted from coverage of the lineup of speakers.
McIver explained that she included the passages from Michelle Obama's speech after listening to Melania Trump read passages from the 2008 address.
"Over the phone, she read me some passages from Mrs. Obama's speech as examples. I wrote them down and later included some of the phrasing in the draft that ultimately became the final speech. I did not check Mrs. Obama's speeches. This was my mistake, and I feel terrible for the chaos I have caused Melania and the Trumps, as well as to Mrs. Obama. No harm was meant."
She said the Trump family rejected her resignation, because, "Mr. Trump told me that people make innocent mistakes and that we learn and grow from these experiences."
"I apologize for the confusion and hysteria my mistake has caused. Today, more than ever, I am honored to work for such a great family," McIver said in the statement.
The Trump campaign has refused to acknowledge the incident as plagiarism, instead slamming the media and insisting it was moving on, with no plans to fire any staffers.
"The speech was very effective and communicated those feelings," Trump campaign chairman Paul Manafort said Tuesday on CNN's "New Day." "The controversy you're talking about is not meaningful at all. She's not a candidate for office. She was expressing her personal feelings about her country and her husband and why he's best for the United States."
Manafort on Wednesday agreed Melania Trump's speech used "similar words" to Obama's and insisted, "I'm not lying about anything."
The Republican National Committee also boosted the Trump campaign's defense, with its communications director Sean Spicer slapping down plagiarism charges by pointing to similar words and themes in everything from John Legend songs to "My Little Pony."
"The media is spending more time doing a forensic analysis of Melania's speech than the FBI spent on Hillary's emails," Trump said in a tweet.
McIver has served as a ghostwriter for the Trumps in the past, helping Donald Trump write some of his books, including "Trump: Think Like a Billionaire."
The New York Times identified McIver as a former ballet dancer and English major.