Trump Jr. Suggested that Obama's speech in Philadelphia on Wednesday night lifted a line from his Republican National Convention remarks, pointing out that both addresses contained the line "That's not the America I know."
"I'm honoured that POTUS would plagiarise a line from my speech last week. Where's the outrage?" Trump Jr. Tweeted.
The charge comes after Melania Trump was criticised for lifting significant portions of her address to the convention from Michelle's first convention speech in 2008.
"And other than the brief sentiment about the version of America known to both men, the context of the statements was very different," the report said.
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"There's so much work to do. We will not accept the current state of our country because it's too hard to change. That's not the America I know. We're going to unleash the creative spirit and energy of all Americans," Trump Jr had said in his convention speech.
"There were no serious solutions to pressing problems, just the fanning of resentment and blame and anger and hate. And that is not the America I know. The America I know is full of courage, and optimism, and ingenuity. The America I know is decent and generous," he had said.
The use of the "America I know" refrain was also a common phrase for former president George W Bush.
Melania had found herself in the midst of an embarrassing plagiarism controversy earlier this month after a prime-time defence of her husband Donald appeared to be lifted in part from a speech given by Michelle Obama at the 2008 Democratic convention.
Trump had termed as an "innocent mistake" the plagiarism surrounding his wife's speech and rejected the resignation by the speech-writer.