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

New York (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."

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