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US President Donald Trump on Tuesday slammed former first lady Michelle Obama's "wrong president" remarks during the Democratic convention, saying he built the "greatest economy in history."

"Somebody please explain to @MichelleObama that Donald J. Trump would not be here, in the beautiful White House, if it weren’t for the job done by your husband, Barack Obama. [Joe] Biden was merely an afterthought, a good reason for that very late & unenthusiastic endorsement," Trump said on Twitter.

"My Administration and I built the greatest economy in history, of any country, turned it off, saved millions of lives, and now am building an even greater economy than it was before. Jobs are flowing, NASDAQ is already at a record high, the rest to follow. Sit back & watch!" he added.

Michelle Obama laid into Trump on Monday, saying he "is the wrong president for our country" and imploring voters to turn out in support of presumptive Democratic nominee Biden even if he is not their first choice.

Trump, she said, "has had more than enough time to prove that he can do the job, but he is clearly in over his head. He cannot meet this moment. He simply cannot be who we need him to be for us. It is what it is."

"If we have any hope of ending this chaos, we have got to vote for Joe Biden like our lives depend on it," Obama said. "This is not the time to withhold our votes in protest or play games with candidates who have no chance of winning. We have got to vote like we did in 2008 and 2012. We have got to show up with the same level of passion and hope for Joe Biden."