"I hope - but am not yet confident - that (North Korea) will take steps that match the concessions Mr. Trump has already made by ending military exercises in South Korea and granting Mr. Kim legitimacy with this summit", Thomas Countryman, a former acting under secretary of state for arms control under President Barack Obama, told Reuters. "So, I think the rhetoric - I hated to do it, sometimes I felt foolish doing it - but we had no choice", he told Hannity.
The president left Singapore after the two leaders signed a document stating Pyongyang would work toward "complete denuclearization of the Korean Peninsula".
Trump also seemed annoyed that USA bomber aircraft make six-plus hour flights from the Pacific island of Guam to the Korean peninsula as part of its exercise routine.
"It's important for us to remember that it's largely words at this point, and that we have to look for actions, particularly from North Korea", Panetta said during an interview with FOX Business' Neil Cavuto on Tuesday. "That's not part of the equation right now".
Trump's comments will be questioned by many in South Korea and beyond, with some seeing in them an effort by North Korea to drive a wedge between Seoul and Washington.
On Tuesday, Trump and Kim announced an agreement committing the U.S.to unspecified "security guarantees" in exchange for the eventual denuclearization of the Korean peninsula.
And what "exactly was the president committing to?" he added.
Exercises with South Korea cover a range of eventualities, including drills with nuclear-capable bombers.
Chairman Kim and President Trump put pen to paper following an historic meeting in Singapore.
But Daniel Davis, a retired army lieutenant colonel and fellow at the Defense Priorities military think tank, said suspending the drills would have no short-term impact on US and South Korean military readiness.
"There is no single change in the suspension of the South-U.S. joint military exercise compared to the past", Nam said.
Trump speaks to Kim as the pair prepare to begin their closed-door talks.
Rep. Ed Royce of California, who is chairman of the House Foreign Affairs Committee, applauded Trump for pursuing peace through diplomacy, but he also said Kim had "gained much" Tuesday, "including an apparent promise" from Trump to suspend military drills.
"But we believe it is necessary to come up with various measures to improve dialogue more smoothly", the Blue House said.