Kelly on Friday held an OTR session with reporters to tell them Trump is likely speculating about staff moves to his pals outside the White House - who are then talking to reporters.
Mr Kelly himself is the subject of rumours that his days on the job are numbered.
CIA Director Mike Pompeo, who was recently named secretary of state, has echoed Trump's denouncing of the 2015 Iranian nuclear agreement between the USA and other world powers.
White House spokesperson Sarah Sanders denied the reports during a media briefing on Friday.
The previous year saw the departure of Trump's first national security advisor Michael Flynn - who lasted just 22 days in his post - as well as chief strategist Steve Bannon, who made it seven months, and Reince Priebus, who stayed in his job for less than six.
Tillerson would only say on Tuesday that he had received a lunchtime call from Trump during the president's cross-country flight, along with a separate call from Kelly - both conversations happening after the tweet heard 'round the diplomatic world.
Israeli soldiers killed in West Bank vehicle attack
Israeli fighter pilots bombed a terror target in central Gaza late Saturday night, the Israel Defense Forces announced. Gaza internal security forces chief Toufik Abou Naim said that the decision was taken by the general prosecution.
Britain says likely that Russia's Putin made decision for nerve agent attack
Britain is expelling 23 Russian diplomats and taking other steps against Russian interests as the two nations' relations plummet. De Bretton-Gordon dismissed that claim as "complete hogwash".
Setback for BJP as TDP quits NDA, moves no-trust motion
The YSR Congress-a regional party in AP- also moved a no-confidence motion against the Modi Government. Such a motion can only be moved with the support of over 50 MPs.
His economic nationalism became the lynchpin of Trump policies, even as many of his other ideas were rebuffed by policy rivals.
In private conversations in recent weeks, Trump has reflected on his desire to reshape the administration.
Mcmaster, a three star general, and President Trump never really gelled.
The president and McMaster have disagreed on a number of issues - including the Iran deal and the USA approach to North Korea - and the national security adviser has also clashed with Kelly and Defense Secretary James Mattis, according to the officials. Officials said personal tensions have led McMaster to be sidelined in some internal discussions, including a recent meeting on Venezuela sanctions, with Kelly taking on a more active role in foreign policy decisions. Secretary of State Rex Tillerson is the latest top official to leave a U.S. administration where turnover has been inordinately high. The president was speaking to friends outside the administration about his frustrations with advisers, Mr Kelly suggested.