NEW YORK—President-elect Donald Trump suggested he would be open to lifting sanctions on Russia and wasn’t committed to a longstanding agreement with China over Taiwan—two signs that he would use any available leverage to realign the U.S.’s relationship with its two biggest global strategic rivals.

In an hourlong interview, Mr. Trump said that, “at least for a period of time,” he would keep intact sanctions against Russia imposed by the Obama administration in late December in response to Moscow’s alleged cyberattacks to influence...