President Barack Obama has accused Donald Trump and the Republicans of peddling fear and falsehoods and said the American people deserved to make important decisions based on fact.

In his first comments about the Republican National Convention, Mr Obama on Friday said he had not had time to watch the events, but had read reports of what was said and claims that were made about crime and immigration, troubled him.

“This idea that America is somehow on the verge of collapse, this vision of violence and chaos everywhere, doesn’t really jibe with the experience of most people,“ he said. “I think most people woke up and the birds were singing and the sun was out.”

Donald Trump addresses delegates during the final day session of the Republican National Convention (AP)

Standing alongside Mexican President Enrique Pena Nieto, Mr Obama said that on two key issues, the Republicans had not told the truth.

“The violent crime rate has been lower during my presidency than at any time in the last three of four decades,” he said. “The violence rate today is lower than when Ronald Reagan was on office. And it is lower than when I came into office.”

On the issue of immigration, a topic on which Mr Trump has built much of his appeal to the US people, Mr Obama said huge resources had been diverted to the borders.

“The rate of illegal immigration to the US is lower by two-thirds then when Ronald Reagan was president,” he said. “We have far fewer people crossing the border than during the 1980s, the 1990s or when George Bush was president. That is a fact.”

Mr Obama’s attack came as the Republicans wrapped up their convention, an event that was beset with controversy over plagiarism, dissent and disunity, and as the Democrats prepared for theirs in Philadelphia next week.

Trump's speech interrupted by protestor

One of controversies to make headlines during the convention was a speech delivered by former presidential candidate, Senator Ted Cruz, who took to the stage and urged people to vote with their “consciences”. The Texas senator, who subsequently said that the New York tycoon had insulted his family, pointedly, declined to endorse Mr Trump.

On Friday, Mr Trump said he would not accept Mr Cruz’s support, even if it were to be offered.

“If he gives it, I will not accept it,” Mr Trump said at a news conference in Cleveland. “I don’t want his endorsement. Just, Ted, stay home, relax, enjoy yourself.”

Mr Trump also returned to another controversy, a claim which first appeared in the National Enquirer magazine and which the tycoon repeated, that Mr Cruz’s father was somehow linked to the assassin of President John F Kennedy, Lee Harvey Oswald. Mr Cruz had scoffed at the suggestion when Mr Trump raised it in the spring.

“I don't know his father. I met him once,” Mr Trump said on Friday.

“I think he's a lovely guy, a lovely guy. All I did was point out the fact that on the cover of the National Enquirer, there was a picture of him and crazy Lee Harvey Oswald having breakfast. Now Ted never denied that it was his father.”

Bloomberg News said that Mr Obama's claim that illegal immigration was at the lowest level in decades was difficult to examine because, by definition, the government was unaware of such border crossings.