President Obama said Friday that Donald Trump's claims in his primetime speech accepting the GOP presidential nomination in Cleveland have no basis in fact.

During a joint press conference at the White House with Mexican President Enrique Peña Nieto, the president was asked for his reaction to the four-day Republican National Convention that wrapped up the previous night.

"I did not watch the convention -- I don't think that's a surprise," Mr. Obama said, adding, "I did read some of what was said. The one thing that I think is important to recognize is 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."

Mr. Obama added that, "Some of the fears expressed throughout the week just don't jive with the facts."

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Responding to Trump's claims Thursday night about a spate of violence and high crime plaguing the U.S., the president said that the violent crime rate domestically "has been lower during my presidency than any time during the last three, four decades."

The president acknowledged that while there has been an "uptick in murders and violent crime in some cities this year," he said that the violent crime rate is "far lower" than it was under President Ronald Reagan and lower than when Mr. Obama first took office in 2009.

On Trump's remarks about illegal immigration in the U.S., Mr. Obama said that the rate of illegal migration into the U.S. today is "lower by two-thirds than it was when Ronald Reagan was president."

"We have far fewer undocumented workers crossing the border today than we did in the 80s, in the 90s, or when George Bush was president," he said. "That's a fact."

"We're not going to make good decisions based on fears that don't have a basis in fact," he added.

The president's remarks came after Trump's speech Thursday night in Cleveland, when he accepted the Republican presidential nomination. The address focused at length on violence, terrorism and a weak immigration system.

But fact-checkers immediately went to work and on many of his statements. Violence and property crime has been falling for decades in the U.S., according to Politifact. The number of police officers also barely rose eight percent since 2015, according to the National Law Enforcement Officers Memorial Fund.

CBS News' Reena Flores contributed to this report.