"Kim appeared to be in control of his government and sounded very reasoned," said Jones, citing information passed on by Clinton and his aides.
"He seemed to be in control of his faculties."
Clinton, who flew to North Korea to obtain the release of two US journalists detained for illegally entering the country, held more than three hours of talks with Kim during his visit.
"North Korea can't continue to make commitments and then violate them and expect to start from where they left off. The ball is in their court"
Susan Rice, US ambassador to the UN
The former US president was the most senior US envoy to visit the North in almost a decade, although Obama administration officials insist the visit was a humanitarian mission carried out by a private individual.
Nonetheless Jones said that during talks with the North Korean leader, Clinton had emphasised on the importance and advantages of denuclearising the Korean peninsula, including the possibility of a dialogue with the US.
"I'm quite sure the former president was very articulate and persuasive that the North Koreans know exactly what the world community, the members of the six party talks expect," he said on NBC television.
"And it's up to them to move forward."
Both Jones and Susan Rice, the US ambassador to the UN, said that Washington was prepared to resume the kind of direct talks held in the latter years of the Bush administration.
In a separate television interview Rice urged the North Koreans "to uphold their international obligations" and resume the international negotiations.
"In that context, we have said that we would be prepared to have a direct dialogue", she said on CNN.
"But North Korea can't continue to make commitments and then violate them and expect to start from where they left off. The ball is in their court."
|North Korea withdrew from nuclear talks after a series of missile tests earlier this year [AFP]
Clinton's visit has come under fire from some prominent conservatives in the US who have criticised it as essentially giving in to North Korean blackmail.
Refuting suggestions that the visit was a propaganda victory for Pyongyang, Jones said the mission had been vetted by South Korea, Japan, China and Russia.
"We had 100 per cent from all these countries," he said, referring to the members of six-party talks.
The Obama administration is trying to coax the North into abandoning its nuclear weapons programme while at the same time moving to enforce tougher UN sanctions against Pyongyang.
North Korea pulled out of the six-party nuclear disarmament talks in April after test-firing a long-range missile.
It followed up the missile launch with a second nuclear test in May, sparking the latest crisis in international efforts to get it to abandon nuclear weapons.