Donald Trump speaks at a campaign rally in Fredericksburg, Va., on Saturday. (Gerald Herbert/AP)

This post has been updated. 

Donald Trump called on Monday for the Clinton Foundation to shut down "immediately" and return money that was donated by countries "they shouldn't be taking money from."

"The Clintons have spent decades as insiders lining their own pockets and taking care of donors instead of the American people," Trump said in a statement Monday morning. "It is now clear that the Clinton Foundation is the most corrupt enterprise in political history. What they were doing during Crooked Hillary’s time as Secretary of State was wrong then, and it is wrong now. It must be shut down immediately.”

Minutes after releasing that statement, Trump called in to Fox News and again called for the foundation to shut down.

"They should give the money back to a lot of countries that we shouldn't be taking and they shouldn't be taking money from — countries that influenced her totally and also countries that discriminate against women and gays and everybody else," Trump said. "I mean, that money — it should be given back. They should not take that money."

When asked whether he thinks the Clintons will do so, Trump responded: "It should happen. Whether or not it will, they're very greedy people, so maybe it won't. But it should happen."

Clinton's campaign has yet to respond to Trump's demand. Clinton's running mate, Sen. Tim Kaine (Va.), mentioned Trump's attack and defended the foundation during an address Monday to the Ironworkers in Las Vegas.

"The foundation … will restructure itself completely if Hillary Clinton is elected president. That’s a pledge," Kaine said. "Donald Trump, on the other hand, has told us nothing about how he’ll deal with the conflicts posed by his business dealings, like the money his company owes to the Bank of China. And I have this to say to Donald Trump … Before you go about attacking a charity, why don’t you come clean about your own business dealings and tell the American people who you are in debt to?”

Trump's own charity — the much smaller Donald J. Trump Foundation — has also taken money from corporations, including NBC Universal, which broadcast his show "The Apprentice." Most of its donations in recent years have come from individuals, including wrestling executives Vince and Linda McMahon. Tax records list no gifts to the foundation from Trump's own pocket since 2008.

Trump's campaign has yet to say if the businessman will immediately shut down his own foundation.

The Clinton Foundation has raised hundreds of millions of dollars for global health initiatives and relief work around the world, but as Clinton runs for president, she has faced questions about how the foundation raised that money, especially during her time as secretary of state. Trump and others have questioned why the foundation accepted tens of millions of dollars from countries that discriminate against women, gays or minorities. Rudolph W. Giuliani, the former mayor of New York City and a prominent Trump supporter, said in an interview Sunday on Fox News that the Clinton Foundation should be indicted for being "a racketeering enterprise."

"She did favors for those very people who gave money to the Clinton Foundation," Giuliani said. “In my definition that was bribery.”

The foundation has denied any wrongdoing. Former president Bill Clinton announced Thursday that if his wife is elected president, the foundation will no longer accept donations from corporations or foreign entities — prompting some to ask why that change doesn't happen sooner. A Washington Post analysis found that under this new rule, more than half of the foundation's major donors would no longer be allowed to contribute. Last week, the Boston Globe editorial board called for the foundation to stop taking donations and, if Clinton is elected, shut down.

During the interview with Fox, Trump was also asked about deporting 11 million immigrants living illegally in the United States, a stance he firmly took last summer but seems to be reconsidering.

"We have to be very firm. We have to be very, very strong when people come in illegally," Trump said. "We have a lot of people that want to come in through the legal process, and it's not fair for them. And we're working with a lot of people in the Hispanic community to try and come up with an answer."

A Fox News host then pressed Trump, asking if his position had changed.

"No, I'm not flip-flopping," Trump said. "We want to come up with a really fair but firm answer. It has to be very firm, but we want to come up with something fair."

David Fahrenthold and John Wagner contributed to this report.