Real-estate mogul Donald Trump has earned the respect of at least one of the Republican presidential nominees he is running against despite the financial setbacks he continues to deal with following the comments he made earlier against Mexicans.

Texas Senator Ted Cruz even promised not to attack Trump, who admitted being surprised when several companies announced they were cutting business ties with the reality TV star over his inflammatory remarks.

"I salute Donald Trump for focusing on the need to address illegal immigration... The Washington cartel doesn't want to address that. The Washington cartel doesn't believe we need to secure the borders," Cruz said, according to News Max.

"I salute Donald Trump for focusing on it. He has a colourful way of speaking. It's not the way I speak, but I'm not going to engage in the media's game of throwing rocks and attacking other Republicans. I'm just not going to do it," he added.

Cruz explained that he shared Trump's opinion against amnesty, saying: "I like Donald Trump. He's bold; he's brash."

Trump called Mexican immigrants "criminals and rapists" in a speech he made when he officially launched his campaign last June 16.

Republican presidential candidates Rick Perry, Chris Christie, and Marco Rubio distanced themselves from Trump's comments, underscoring their recognition of the fact that they need to earn the support of Latino voters.

Meanwhile, former Florida Governor Jeb Bush said he was personally offended by Trump's comments, saying the real-estate mogul does not represent the Republican Party and that his opinions are outside of what Republicans think.

"No one suggests that we shouldn't control our borders—everybody has a belief that we should control our borders. But to make these extraordinarily ugly kind of comments is not reflective of the Republican Party," Bush said, according to Washington Post.

"Trump is wrong on this. He's doing this to inflame and to incite and to get to draw attention which just seems to be the organisation principle of his campaign. It doesn't represent the Republican Party or its values," he added.

Bush, whose wife is from Mexico, made his comment about Trump during the two parades he attended in celebration of Independence Day in the first-in-the-nation primary state.

But Trump stood by his statement while firing back at his critics, blasting his opponents through a series of tweets to his 3.1 million followers on Twitter on Sunday.

He urged Rubio to "stand up for US" while commenting that "Bush will never secure our border or negotiate great trade deals for American workers."

The crime is raging and it's violent. And if you talk about it, it's racist," Trump told Fox News.

He also admitted surprise when NBC and Univision decided not to air the Trump-owned Miss Universe Pageant as Macy's announced that it will be dropping his signature clothing line.

Earlier, New York Democratic Mayor Bill de Blasio ordered a review of Trump's city contracts and Nascar is moving an annual banquet from the Trump National Doral resort in Miami.

"I didn't know it was going to be this severe. I am a whipping post," he added according to Fox News.