JUDY WOODRUFF: But first:
The U.S. secretary of state
visited North Korea yesterday to

continue negotiations
with a regime there over
its nuclear program.

It is a process that has
seen its ups and its downs.

And, as John Yang reports,
this visit produced
some guarded optimism.

JOHN YANG: It was all smiles
around the table for a Sunday
lunch in Pyongyang, where North

Korea's nuclear arsenal
was the main menu item.

Later, Secretary of State Mike
Pompeo reported significant
progress in his talks with North

Korean supreme
leader Kim Jong-un.

MIKE POMPEO, U.S. Secretary
of State: We had a good,
productive conversation.

As President Trump has said,
there are many steps along the
way, and we took one of them

today.

JOHN YANG: The North's
state-run television
echoed that positive tone.

The two sides agreed to
establish working-level
talks on a second
summit between President

Trump and Kim.

Pompeo also told reporters
that the North agreed to allow
inspectors at a nuclear test

site the North says it
demolished last spring.

The administration has
expressed doubts that the site
had actually been destroyed.

Siegfried Hecker is former
director of the Los Alamos
National Laboratory.

He's visited North
Korea several times.

SIEGFRIED HECKER, Former
Director, Los Alamos
National Laboratory:
There had been so much

skepticism about whether what
the North Koreans did actually
would make a difference or not,

whether it would make it
easy for them to test.

So it's a big deal to actually
let someone come in and to
evaluate whether that really

sets back the test
site significantly.

It's an important
confidence-building measure,
as far as I'm concerned.

JOHN YANG: President
Trump's confidence is
already running high.

He recently expressed a fondness
for the North Korean leader he
once derided as Little Rocket

Man.

DONALD TRUMP, President
of the United States:
We fell in love now.

OK?

(LAUGHTER)

DONALD TRUMP: No, really.

He wrote me beautiful letters.

JOHN YANG: The president's top
advisers have remained more
skeptical of shifting from talk

in 2017 of fire and
fury to falling in love.

Instead, they insist
U.S. sanctions will
stay in place until the
North's nukes are gone.

China's support is also
critical for any North
Korean nuclear disarmament.

But maintaining Beijing's
support is complicated
by a growing trade war
and other deep tensions.

That was clear today as
Pompeo met with Chinese
Foreign Minister Wang Yi.

WANG YI, Chinese Foreign
Minister (through translator):
We urge the United States to

stop these kinds of
mistaken actions.

We believe China and the
U.S. should stick to the
correct path of cooperation.

MIKE POMPEO: I regret that the
strategic dialogue between our
two countries was something that

you all chose not to undertake.

JOHN YANG: China's role aside,
there's no framework yet for
dismantling North Korea's

nuclear arsenal.

But Siegfried Hecker notes
that Pyongyang has put aside
further nuclear testing.

SIEGFRIED HECKER: No testing
means they will not be able
to improve the sophistication

of their nuclear weapons.

And particularly what I would be
worried about it is making the
weapons smaller or to continue

to develop the hydrogen
thermonuclear bomb capabilities.

JOHN YANG: The next steps are
unclear, including the possible
timing of that second summit

between the two leaders.

For the "PBS NewsHour,"
I'm John Yang.