The White House brushed off claims by actor Antonio Sabato Jr. that Obama is "absolutely" a Muslim and poked fun at former Mayor Rudy Giuliani's intense delivery of his address on national security, crime and race relations.

"I don't make much of those claims," presidential press secretary Josh Earnest said flatly, in response to a question about Sabato's accusation that Obama is a Muslim. Sabato made that claim after his Monday night speech at the Republican National Convention.

Turning to Giuliani's fiery RNC speech, Earnest remarked that he did hear some of it, and said "it was difficult not to hear given the volume at which it was delivered."

"I'll let other people sort of assess the effectiveness of his delivery," Earnest remarked before defending Obama's national security record, which Giuliani impugned during his primetime address in Cleveland.

"I think what you've heard me acknowledge, what the president has acknowledged over the last couple of weeks, is the kind of violence that we've seen in our streets is unsettling — and there's obviously been a lot to debate about what we can do about it," Earnest said. "I think the president continues to be confident, however, in these unsettling moments, that our country is far more united that it might seem and the kinds of divisions that are on display in our political system aren't reflective of the unity that I think most Americans feel."

Earnest chose not to focus on polls showing people feel less safe, and instead said the killing of police in Dallas and Baton Rouge has brought people together.

"All Americans of all races were deeply disturbed by the killings of police officers in Dallas and Baton Rouge over the last week and a half," Earnest said. "You've seen strong expression of support even by people who have been protesting about isolated incidents of police misconduct, saying that they condemn this violence targeting police officers … at the same time we've seen Americans of all races express concerns about the persistent racial disparities in our criminal justice system."

Polls show, however, that after the police killings in Dallas and Baton Rouge, as well as the slayings of two black men in Minnesota and Louisiana over the last two weeks, a majority of Americans believe race relations have gotten worse under Obama.

Sixty percent of respondents in a new Rasmussen survey say racial divisions have increased during Obama's time in office. That number is up 18 points from two years ago, and just 9 percent of those polled said they thought race relations had improved.

In addition, roughly two-thirds of Americans are bracing for a terrorist attack and believe the U.S. is doing badly in its fight against the Islamic State, according to a CBS New/New York Times poll released July 15.