WASHINGTON, March 28 (Xinhua) -- The United States on Wednesday hailed the positive developments on the Korean Peninsula issue, after the just-concluded visit to China by the Democratic People's Republic of Korea (DPRK)'s top leader Kim Jong Un.

At the invitation of Chinese President Xi Jinping, Kim paid an unofficial visit to China from Sunday to Wednesday.

U.S. President Donald Trump tweeted later that there is a good chance that Kim will do "what is right for his people and for humanity."

"For years and through many administrations, everyone said that peace and the denuclearization of the Korean Peninsula was not even a small possibility," Trump said, adding he looks forward to his meeting with Kim.

Trump noted that he had received a message from Xi that his meeting with Kim went very well.

U.S. State Department spokesperson Heather Nauert said later on Twitter that Kim's visit to China was "an unprecedented, historic step in the right direction."

"We look forward to sitting down with Kim Jong Un to talk about a better future for his people," Nauert tweeted.

White House spokesperson Sarah Sanders also said on Wednesday in a press briefing that "significant progress" has been made on Korean Peninsula issue, and that "things are moving in the right direction."

Sanders said the White House was "cautiously optimistic" about the development of the situation, referring to Kim's visit and his meeting with Xi.

"We feel things are moving in the right direction," she said. "You saw him leave for the first time to -- since becoming the leader of North Korea -- leaving his country for the first time for that meeting."

She added that the United States is "going to continue moving forward in this process in hopes for a meeting down the road" between Kim and Trump.

Washington would like to see the Kim-Trump meeting, she said. "Obviously this is something of global importance and we want to make sure that it's done as soon as we can, but we also want to make sure it's done properly."

"We're working towards that goal," said Sanders. "As we've said before, the North Koreans have made that offer and we've accepted, and we're moving forward in that process."