Kim has labeled the exercises practice for an invasion of North Korea.
Trump's decision to halt, at least temporarily, joint US-South Korean military exercises - which the US president called "war games" - must have been welcome in Beijing, the sources suggest.
On Monday, the South Korean defense minister said the issue is still being discussed.
White added: "We are still coordinating additional actions. Nothing has yet been decided, and it is still in discussion".
Trump said via Twitter on Sunday that it was his initiative to suspend military drills - a step North Korea has long sought.
"That was my offer" to North Korean leader Kim Jong-un, he said.
Comedian's father speaks out after she was murdered while walking home
After the comedians and the public in social networks commemorates Dixon, the country began a debate about violence against women. Ms Douglas said she was motivated to organise a Perth vigil after hearing about superintendent Clayton's statement.
Trump threatens to impose more trade tariffs on China
Trump has been feuding, including Canada and the European Union. "I reminded him that's not fair competition", Pompeo said. Pompeo raised the trade issue directly with China last week, when he met in Beijing with President Xi Jinping and others.
Dutch 'Pink Pop' festival: One dead in bus hit-and-run
A festival that was headlined by Bruno Mars ended in tragedy after a van ploughed into a crowd of people leaving one person dead. The street where it happened and two exits from the festival site were closed following the crash.
Critics of the denuclearization agreement reached in Singapore between Trump and Kim say it lacks important details.
North Korea has always reacted to the Ulchi exercises with belligerence and often its own demonstrations of military capability. In the context of North Korea's strategic forces, "launch sites" can be a bit of a misnomer.
South Koreans are much more optimistic than Japanese people about the prospects for North Korean denuclearization, an annual survey showed Monday, as a series of summits this year have led to a dramatic defusing of tensions.
Trump's decision to suspend the exercises, coupled with the vague joint statement issued after his summit with Kim, have reinforced fears in South Korea that the North is attempting to take advantage of a USA president who appears to care less about the traditional alliance than his predecessors.
Defense officials are also scrambling to pull together cost estimates for the various exercises with South Korea to inform Trump's assertion that the suspension will save an enormous amount of money. This compares to the 60 nuclear warheads North Korea claims to possess.
Japan's Chief Cabinet Secretary Yoshihide Suga said on Tuesday there would be no changes to joint drill plans between the United States and Japan, both of which also engage in regular deterrence exercises against North Korea. That would mean that even if North Korea did conduct some kind of ceremony to "disable" a previously used launch site, it would effectively be meaningless given that these kinds of road-mobile launchers are created to enable launch from a variety of locations. It also involves agreeing to destroy all its nuclear weapons, accepting limits on ballistic missiles and other threatening weapons and destroying its weapons of mass destruction.
Amid fears the summit would weaken the worldwide coalition against the North's nuclear programme, US Secretary of State Mike Pompeo stressed after the meeting that sanctions would remain in place until North Korea's complete denuclearisation.