Friday: The US president warns that military solutions are "locked and loaded" should North Korea "act unwisely".
In response, Mr Trump said North Korea should expect "big, big trouble" if anything happened to Guam.
He said the USA has a "pretty good idea" of North Korea's intentions, but he declined to provide specifics.
And Pompeo said he fully expected Kim to continue to oversee missile tests and seek to advance the North Korean nuclear program in an effort to shore up the country's ability to strike the mainland United States with a nuclear weapon.
The top US military officer, Marine Corps Gen. Joseph Dunford, is traveling in Asia and expected to meet with leaders in South Korea, Japan and China.
"We've seen the Chinese now say for among the first times that they believe the correct answer has to be a denuclearized peninsula", Pompeo said on "Fox News Sunday". Dunford, the chairman of the Joint Chiefs of Staff, told reporters traveling with him that he aims to "sense what the temperature is in the region".
"We're all looking to get out of this situation without a war", Dunford said.
Guam is telling its citizens how to survive a nuclear attack
US President Donald Trump has told Guam Governor Eddie Calvo over the phone that "You are safe". Despite tensions and talk of war, life on the streets of the North Korean capital remains calm.
"The United States military is locked and loaded every day, and especially those who are on the front lines of freedom", said McMaster, who's also an Army lieutenant general.
Earlier this week, the Trump administration also imposed new sanctions on Venezuela, targeting members of the new all-powerful constituent assembly.
Meanwhile, North Korea said on Saturday that almost 3.5 million workers, party members and soldiers volunteered to join or rejoin its army to resist new U.N. sanctions and to fight against the United States in the current geopolitical tension between Pyongyang and Washington.
Tensions between North Korea and the United States have racheted up in recent weeks.
"When I served in Korea many years ago as the director of intelligence USA forces in Korea, what I was anxious about was an incendiary event getting out of hand", Clapper added.
North Korea said on Thursday that plans would be completed by mid-August to fire four intermediate-range missiles to land near the U.S. Pacific island of Guam, 2,175 miles away.
"President Trump inherited a mess", Graham said.
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