US Republican presidential nominee Donald Trump has slammed President Barack Obama's speech in support of Hillary Clinton at the Democratic National Convention, accusing the president of describing a "world that doesn't exist."

Speaking at the packed Democratic National Convention center in Philadelphia, Pennsylvania on Wednesday night, Obama strongly endorsed the Democratic presidential nominee as his successor, saying Hillary is more qualified to be president of the United States than Bill Clinton or himself.

Obama also denounced Trump, saying: "America is already great. America is already strong. And I promise you, our strength, our greatness, does not depend on Donald Trump." He also accused Trump of having a "deeply pessimistic vision" of the country.

Trump on Thursday tweeted that almost three-quarters of Americans think their country is “going in the wrong direction”.

“President Obama spoke last night about a world that doesn’t exist. 70% of the people think our country is going in the wrong direction,” he wrote.

The billionaire businessman also ridiculed Obama by re-posting a link to a video revealing that the president referred to himself 119 times in the convention speech.

US President Barack Obama delivers remarks on the third day of the Democratic National Convention at the Wells Fargo Center, July 27, 2016 in Philadelphia, Pennsylvania. (AFP photo)

Earlier, Trump’s campaign dismissed assaults by Democratic leaders at the Democratic National Convention as “empty rhetoric”.

Trump’s senior policy adviser, Stephen Miller, said the Democratic Party is obsessed with Trump but they “offered no solutions.”

"They described a vision of America that doesn't exist for most Americans, including the 70 percent of Americans who think our country is on the wrong track,” Miller said. “Never has a party been so disconnected from what is happening in our world.”

Miller said Democrats do not want to deal with reality. “They spoke in cheap, petty terms beneath the dignity of a convention.”