"If China is not going to solve North Korea, we will. That is all I am telling you," he said in an interview with UK newspaper the Financial Times.
Pressed on whether he thought he could succeed alone, he replied: "Totally."
Mr Trump was speaking ahead of a scheduled visit from Chinese President Xi Jinping this week.
"China has great influence over North Korea. And China will either decide to help us with North Korea, or they won't. And if they do that will be very good for China, and if they don't it won't be good for anyone," Mr Trump told the FT.
Asked if he meant "one-on-one" unilateral action, Mr Trump said: "I don't have to say any more."
He did not give any further details on what action he would take.