JUDY WOODRUFF: But first: Two days after North Korea's sixth nuclear test, the war of words and the war games continued today.
But President Trump's recent statements targeting South Korea have led to growing concerns there. William Brangham reports.
WILLIAM BRANGHAM: South Korean warships conducted live-fire drills off the Korean Peninsula today, the latest show of military force to try and deter North Korea.
The North answered with more defiance. Its envoy called its weekend nuclear test a — quote — "gift package to the U.S." from his country, which is known officially as the Democratic People's Republic of Korea, or DPRK.
HAN TAE SONG, U. N. Ambassador, North Korea: The U.S. will receive more gift packages from my country as long as it relies on reckless provocations and futile attempts to put pressure on the DPRK. Pressure or sanctions will never work on my country.
The DPRK will never under any circumstance put its nuclear deterrence on the negotiating table.
WILLIAM BRANGHAM: Russian President Vladimir Putin, at a conference in China, also warned against pushing the North Koreans too hard. He said military action could set off a global catastrophe, and that new sanctions won't help either.
PRESIDENT VLADIMIR PUTIN, Russia (through interpreter): The use of all types of sanctions in this particular case is useless and inefficient. As I have told one of my colleagues yesterday, they will rather eat grass than abandon this program if they do not feel safe.
WILLIAM BRANGHAM: Later, Russian Foreign Minister Sergei Lavrov said Moscow will consider a U.S. resolution in the U.N. Security Council, provided it focuses on a diplomatic solution.
Meanwhile, President Trump is also putting pressure on South Korea. He's again threatened to pull out of a five-year-old trade deal with the south, something that a bipartisan group of U.S. lawmakers today urged against. And over the weekend, the president also pushed them to get tougher, tweeting: "South Korea is finding that their talk of appeasement with North Korea will not work."
But that message may be driving a wedge between the two allies.
JEAN LEE, Wilson Center: South Koreans were very preoccupied by the fact that it took 34 hours for President Moon Jae-in and President Donald Trump to even have a phone conversation after that nuclear test.
WILLIAM BRANGHAM: Jean Lee ran the Associated Press's bureau in North Korea and is now a fellow at the Wilson Center in Seoul, South Korea.
JEAN LEE: South Koreans were incredibly offended by that.
To people here, the comments on the approach on that president is taking seem incredibly outdated and offensive. So, I think that that is some of the reaction that I'm getting from younger South Koreans here in Seoul.
WILLIAM BRANGHAM: At the White House, though, officials today defended the get-tough approach.
SARAH SANDERS, White House Press Secretary: Now is not the time for us to spend a lot of time focused on talking with North Korea, but putting all measures of pressure that we can, and we're going to continue through that process.
WILLIAM BRANGHAM: Meanwhile, there's talk in South Korea of building up its own conventional arsenal and perhaps even acquiring its own nuclear weapons.
In a new tweet today, President Trump confirmed he's letting South Korea and Japan buy sophisticated U.S. weapons.
For the PBS NewsHour, I'm William Brangham.