Washington (CNN) A dispute over North Korea has once again laid bare the apparent rift between the White House and the top US diplomat, leading to behind-the-scenes scrambling this week by aides meant to avoid mixed signals about the world's tensest standoff.

Even as staff members scurried to clean up what appeared to be diplomatic differences, however, President Donald Trump himself remained unperturbed over the dust-up, according to an official familiar with the situation -- an attitude people close to the President say reflects his confidence that foreign leaders and members of his administration understand that he's in charge.

White House staffers were caught off guard this week by Secretary of State Rex Tillerson's offer during a public forum on Tuesday to "sit down" with North Korea "and see each other face-to-face." His remarks prompted the White House to take the unusual step of releasing a statement to reporters attempting to clarify the administration's position.

But by the time Trump and Tillerson sat down for lunch Thursday in the small private dining room abutting the Oval Office, Trump did not reprimand Tillerson for his remarks. The two men met privately before sitting down for their meal.

Anxieties exist

The situation underscores the anxieties within the administration at maintaining a united front against North Korea, even as Trump's advisers continue to hold differing viewpoints on how best to confront the rogue regime. Some analysts and experts have written off Trump's team as demonstrating a muddled message. But administration officials insist they all share the same goal of a denuclearized North Korea.

West Wing staffers were surprised at Tillerson's remarks since they believed Trump has been explicit in his insistence the time is not right for talks with Pyongyang, particularly after an apparent dispute earlier this year between the President and Tillerson on the matter.

"I told Rex Tillerson, our wonderful secretary of state, that he is wasting his time trying to negotiate with Little Rocket Man," Trump wrote at the beginning of October after Tillerson raised the prospects of talks with North Korea. Trump uses "little rocket man" as an insult to North Korean leader Kim Jong Un.

On Tuesday, some of Trump's aides found it odd that Tillerson would continue reiterating a conciliatory position on talks, even after the dispute with Trump earlier this year.

"We are ready to have the first meeting without precondition," Tillerson said at the Atlantic Council in Washington, in what seemed to amount to a direct public invitation for North Korea to put aside an escalating cycle of tests and taunts to engage in diplomacy.

"Let's just meet, and we can talk about the weather if you want. Talk about whether it's going to be a square table or a round table, if that's what you are excited about. But can we at least sit down and see each other face to face, and then we can begin to lay out a map, a road map of what we might be willing to work towards," he said.

Concern about confusion

JUST WATCHED Tillerson: US ready to talk to North Korea Replay More Videos ... MUST WATCH Tillerson: US ready to talk to North Korea 01:12

Some aides were concerned that Tillerson's comments on Tuesday would confuse allies, many of whom are pressing the US to agree to talks with North Korea. Trump has been insistent on maintaining pressure on the regime through sanctions and joint military exercises and does not want to show any cracks in that pressure.

Aides to Tillerson, however, disputed the notion that the diplomat was trying to make new policy on North Korea in his comments. And they pointed to his planned remarks Friday at the United Nations Security Council as evidence of his attempts to maintain pressure on North Korea, keeping with the President's objectives.

"There is never full agreement on any one approach," said one aide. "But the secretary knows that he has the full support of the President. He has a very close relationship with the President. They speak often and they speak candidly with each other."

"That is the joke of it," the aide continued. "It is the opposite of what people think."

A State Department official reiterated this week that there is no daylight between the State Department and White House on North Korea, acknowledging it is Trump and his circle of advisers at the White House that are ultimately driving the policy.

Indeed, Tillerson is viewed by some White House aides to have been marginalized in the policy-making process on North Korea, and some advisers to Trump have begun openly speculating about a replacement plan for Tillerson that involves moving CIA Director Mike Pompeo to the State Department post.

Not leaving

JUST WATCHED Trump and Tillerson's tense relationship Replay More Videos ... MUST WATCH Trump and Tillerson's tense relationship 01:50

Tillerson, however, has insisted both in public and private that he's not leaving, even as some White House aides grow frustrated at his diplomatic efforts that seem to be at odds with Trump's. And Trump, at least for now, does not appear to be pushing him to the exits.

On Thursday, State Department spokeswoman Heather Nauert said Trump and Tillerson "spent two hours together."

"They met together then had lunch with (Defense) Secretary Mattis," Nauert said.

And even as White House staffers expressed concern about Tillerson's remarks, few believed Trump himself to be disturbed. Trump, one official said, isn't bothered by Tillerson expressing his own views, even if they appear contradictory to his own.

Trump has said that he makes the final decisions on foreign policy, and believes foreign leaders and his members of his own administration know that. He conveyed as much on Twitter earlier this month, at the same time refuting reports that he was preparing to replace Tillerson.

The media has been speculating that I fired Rex Tillerson or that he would be leaving soon - FAKE NEWS! He's not leaving and while we disagree on certain subjects, (I call the final shots) we work well together and America is highly respected again!https://t.co/FrqiPLFJ1E — Donald J. Trump (@realDonaldTrump) December 1, 2017

"He's not leaving and while we disagree on certain subjects, (I call the final shots) we work well together and America is highly respected again!" Trump wrote.

Some former US officials have raised doubts over whether Tillerson and the White House are on the same page.

"It is somewhere between confusing and worrisome," according to Evan Medeiros, a former National Security Council senior director for Asia.

"The State Department and White House should be in lockstep when it comes to issues like negotiating with North Korea," he added. "So if the White House is not backing up Tillerson, it suggests that Tillerson himself is trying to push the White House in the direction of just getting talks started, and perhaps Tillerson doesn't fully appreciate all the downside risks associated with talks without any kind of presteps or preconditions."