Republican presidential nominee Donald Trump vowed Saturday to deport "criminal illegal immigrants ... within one hour" of his inauguration if he is elected in November. 

Trump's promise, made during a speech in Iowa, came after several days of accusations that the real estate mogul had backed down on his signature issue to appeal to undecided general election voters. 

In an appearance on Fox News' "Hannity" Tuesday night, Trump told a town hall audience in Austin, Texas that he was open to "softening" current federal immigration law.

"There could certainly be a softening because we're not looking to hurt people," Trump said at the time. "We want to follow the laws, you know, we have very strong laws in this country. And you know Bush, and even Obama, sends people back. Now, we can be more aggressive on that but we want to follow the laws."

On Saturday, however, Trump said the media had "missed the whole point on immigration ... They take phrases and statements, chop them up, take them out of context and discuss them for days."

Trump also said that he was developing an "exit-entry tracking system to ensure those who overstay their visas, that they're quickly removed." The proposal echoed the language of Trump's former primary rival, New Jersey Gov. Chris Christie, who is now advising him.

"My priority is the well-being of 300 million American citizens, including millions of Hispanic citizens and legal residents who want a secure border, and I mean secure," said Trump, who maintained his vow to build a wall across America's southern border.

Trump touched off controversy during the GOP primary race by vowing to use a  "deportation forceā€ to round up and deport millions of illegal immigrants.

However, during his appearance on "Hannity" this week, Trump said his administration would be willing to "work with" illegal immigrants.

"They'll pay back-taxes, they have to pay taxes, there's no amnesty, as such, there's no amnesty, but we work with them," Trump said.

The Republican nominee's campaign has twice canceled scheduled speeches where Trump was expected to detail his immigration policy. Trump told Fox News Friday that he would deliver such a speech within the next two weeks. 

The Associated Press contributed to this report.