U.S. Secretary of State Rex Tillerson said diplomatic efforts to rein in Pyongyang's nuclear weapons program "will continue until the first bomb drops," as the U.S. and South Korean navies kicked off a massive, five-day joint military exercise Monday in the waters surrounding North Korea.

The statement by America's top diplomat came despite a series of recent tweets by President Donald Trump that seemed to rule out diplomacy, including one that said Tillerson was "wasting his time trying to negotiate with Little Rocket Man," a mocking reference to North Korean leader Kim Jong Un.

Speaking Sunday on CNN's "State of the Union," Tillerson was asked if Trump's tweets had undermined any diplomatic push for solving the North crisis.