Meredith McIver, a staff writer for the Trump Organization, said she had inserted passages into Melania Trump's speech that resembled parts of a 2008 speech by first lady Michelle Obama.
"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," McIver said in a statement.
She said Melania Trump had read passages from Michelle Obama's speech to the 2008 Democratic National Convention over the phone to her as examples.
Ms McIver then wrote them down and later included some of the phrasing in a draft that became Melania Trump's speech on Monday night.
It was Mrs Trump's first speech of the campaign and she had the help of a speechwriting team.
When the accusations of copying first emerged, Mr Trump's campaign chairman Paul Manafort said it was absurd to think Mrs Trump would plagiarise parts of her speech, given it would be watched by tens of millions of people.
Speaking with CNN, he accused Mr Trump's Democratic rival Hillary Clinton of being behind the claims. "This is once again an example of when a woman threatens Hillary Clinton, she seeks out to demean her and take her down. It's not going to work."
Democrats said the Trump campaign's various explanations over the next 48 hours showed his team was not ready for prime time, all the more embarrassing because Mr Trump has accused the Mrs Clinton of being untrustworthy.
In his first comments addressing the speech controversy, Trump argued early on Wednesday that the fuss could in fact be a plus for his campaign.
"Good news is Melania's speech got more publicity than any in the history of politics especially if you believe that all press is good press!" Trump wrote on Twitter.
In a potentially embarrassing admission for the Trump campaign, speechwriter McIver said in her statement that Michelle Obama is a person that Melania Trump "has always liked."
A small section of Melania Trump's roughly 15-minute speech, a highlight of the opening day of the convention in Cleveland, was similar to Michelle Obama's 2008 speech in support of Barack Obama, then a US senator campaigning for president.
Under pressure to explain what had happened and who was to blame, Trump's people offered different versions of events on Monday and Tuesday.
Hours before giving the speech on Monday, Melania Trump told NBC's "Today" that she wrote it with as little help as possible. But Mr Manafort told CBS' This Morning on Tuesday that it was a collaboration with speechwriters.
Ms McIver said Donald Trump and his family rejected an offer from her to resign after the speech controversy broke. The Trump Organization is owned by Donald Trump.
Mr Trump planned to make a display of solidarity on Wednesday with his running mate, Mike Pence, a social conservative who is at odds with the New York businessman on many issues. Mr Pence, the Indiana Governor, is the keynote speaker the third day of a convention that ends the following day when Trump accepts the nomination.