WASHINGTON -- President Trump got word of a secret Beijing meeting between the leaders of China and North Korea just a few hours before it was made public. On Wednesday, Mr. Trump seemed anxious to meet Kim Jong Un for himself.

"We're going to be cautiously optimistic ... we want to make sure that it's done as soon as we can, but we also want to make sure it's don't properly and we're working toward that goal," White House press secretary Sarah Huckabee Sanders said.

The renewed optimism came after Kim made a secret visit to Beijing for his first meeting with Chinese President Xi Jinping. It was his first trip outside North Korea since coming to power nearly seven years ago.

He used the appearance to publicly confirm he is willing to hold a summit with Mr. Trump and, according to Chinese media, vaguely committed to denuclearize under certain conditions.

China's ambassador carried a personal message from Xi to the White House on Tuesday with details of Kim's offer. His Beijing visit seems to have repaired North Korea's relationship with China, which had been damaged by China's support for sanctions on North Korea's accelerating nuclear program.

"Now he looks like a leader of a normal country. It legitimizes him," former CIA analyst Su Mi Terry said.

On Wednesday, Mr. Trump predicted on Twitter that there is a "good chance that Kim Jong Un will do what is right for his people and for humanity. Look forward to our meeting!"

For years and through many administrations, everyone said that peace and the denuclearization of the Korean Peninsula was not even a small possibility. Now there is a good chance that Kim Jong Un will do what is right for his people and for humanity. Look forward to our meeting! — Donald J. Trump (@realDonaldTrump) March 28, 2018

However, there are already signs that North Korea may not be acting in good faith. Satellite images appear to show a new reactor -- possibly for enriching plutonium -- coming online.

Satellite image shows apparent nuclear reactor going up in North Korea. CBS News

"Kim Jong Un can say to himself, 'I'm already established. I'm already a nuclear power. I already have 60 nuclear warheads ... I'm 90-95 percent done with my nuclear program. So I'm in a position of strength coming into this negotiation,'" Terry said.

While North Korea pledged to hold off on any tests, it continues to develop its nuclear program. The White House and U.S. intelligence -- led by CIA director Mike Pompeo, who has not yet been confirmed as secretary of state -- are laying the groundwork for the landmark summit.