A day after President Donald Trump scrapped a planned June 12 summit with Kim Jong Un, the President, White House, and State Department made clear that U.S. officials continue to be open to further contacts with their North Korean counterparts, seeing if there is a way to get talks back on track to rein in the nuclear weapons program of the Pyongyang regime.

"We always knew there would be twists and turns leading up to this meeting on June 12," said State Department spokeswoman Heather Nauert.

"We never expected it to be easy, so none of this comes as a surprise to us," Nauert added.

On Friday afternoon, officials said that Secretary of State Mike Pompeo had spoken by phone with the South Korean Foreign Minister, to discuss what the next steps might be - after the June 12 Trump summit with Kim Jong Un was cancelled.

Earlier in the day, the President expressed hope that talks could resume on the effort to denuclearize the Korean Peninsula, as allies of Mr. Trump argued he made the right move in walking away from the summit at this point in time.

"I don’t know where we will meet, when we will meet, or even if we will meet.....but I do believe President Trump is going to end the North Korean nuclear program," said Sen. Lindsey Graham (R-SC).

But as Graham and others acknowledged on Friday, it wasn't clear whether progress might be made, or how.

From both the U.S. side, and the North Korean side, there was no resumption on Friday of some of the more bellicose rhetoric that had marked the long distance relationship between Mr. Trump and Kim Jong Un, as Pyongyang officials said they were open to further talks and the President said he was not giving up.

"Everybody plays games," the President told reporters in talking about the art of negotiation.

"We weren't getting the right signals previously, so hopefully we will in the future," Nauert told the White House Pool reporter, as President Trump gave the commencement address at the Naval Academy on Friday.

"But we didn't want to go to a meeting just for the sake of going to a meeting," Nauert added. "There had to be something to come out of it. so we weren't getting the right signals."