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Story highlights

"China should solve that problem and we should put pressure on China to solve the problem," Trump told CNN's Wolf Blitzer

Trump also hit Texas Sen. Ted Cruz over immigration

(CNN) —  

Donald Trump says he’s sick and tired of the United States acting as the world’s policeman.

The day after North Korea claimed that it had conducted its first-ever successful hydrogen bomb test, the Republican presidential front-runner pointed the finger at China. His message: Pyongyang is Beijing’s problem to fix.

“China should solve that problem and we should put pressure on China to solve the problem,” Trump said in a wide-ranging interview with CNN’s Wolf Blitzer on “The Situation Room” Wednesday at Trump Tower in midtown Manhattan. “If they don’t solve that problem, we should be very tough on them on trade – meaning, start charging them tax or start cutting them off. You’d have China collapse in about two minutes.”

Trump also demanded on Wednesday that South Korea pay up. The United States has thousands of troops stationed in South Korea, which has been in a state of armistice with North Korea since the 1950s.

“South Korea is a money machine. They pay us peanuts,” Trump said. “South Korea should pay us and pay us very substantially for protecting them.”

Just weeks away from the Iowa caucuses, the real estate developer continues to lead in national polls. But he faces a serious threat in Iowa from Ted Cruz, the Texas senator whose poll numbers have climbed in recent weeks in the state which has a sizable evangelical population.

On Wednesday, Trump hit Cruz on immigration, accusing the senator of having backed amnesty for undocumented immigrants.

“Ted was in favor of amnesty. Him and Marco Rubio have been fighting about who’s weaker,” Trump told Blitzer.

He said he disagreed with Cruz on whether undocumented immigrants should be allowed to return to the United States after being deported.

“I think he should let them come back. If they’re very good people you let them come back legally. I want people to come back,” Trump said. “I’m building a wall but I want people to come in. I want immigrants to come in.”

Trump stirred up fresh controversy this week when he raised questions about Cruz’s eligibility to be president.

Pointing to the fact that Cruz was born in Canada, Trump told The Washington Post: “Republicans are going to have to ask themselves the question: ‘Do we want a candidate who could be tied up in court for two years?’ That’d be a big problem.”

Asked on Wednesday whether he believes Cruz is a natural-born citizen, Trump answered: “I don’t know.”

“To be honest – and I like him a lot and I don’t like the issue. I don’t even like bringing it up,” he said.

However, he noted that the fact that Cruz was born in Canada makes him vulnerable to lawsuits, and could ultimately spell trouble for the Republican Party. He proposed that the senator seek a “declaratory judgment” from federal court to settle the matter.

“If Ted should eke it out – and I hope that doesn’t happen – and he’s got this cloud over his head, I don’t think it’s going to be possible for him to do very well,” Trump said.

This week was not the first time that Trump has waded into “birther” territory. He’s famous for having questioned President Barack Obama’s place of birth, repeatedly insisting that the President publicly release his birth certificate.

Pressed on whether he currently believes Obama is a natural-born citizen, Trump on Wednesday declined to say.

“Who knows, who knows, who cares right now,” he said. “I have my own theory on Obama someday. I’ll write a book. I’ll do another book, it’ll do very successfully.”