(CNN) A scramble by White House aides to respond to the brewing controversy over Donald Trump Jr.'s meeting with a Russian lawyer may have exposed those aides to special counsel scrutiny.

They can now be called on by investigators led by Special Counsel Robert Mueller to explain what they may have learned about the meeting that the President's eldest son, Trump Jr., his son-in-law, Jared Kushner, and then-Trump campaign chairman Paul Manafort had with the Russian lawyer during the 2016 campaign.

White House aides and Kushner's legal team began strategizing in late June over how to manage the disclosure of newly discovered emails setting up that meeting, according to sources close to Kushner's legal team.

Their public relations efforts culminated in a series of stumbles over the weekend in response to inquiries from The New York Times , which was working to publish a story about the meeting. Initial statements by Trump Jr., who organized the meeting, were undermined by more reporting from the paper.

Some of the President's closest aides, who were traveling with him back from Europe, then helped strategize about a response for Trump Jr., according to people briefed on the matter. The Times first reported on the crafting of the statement.

A sensitive legal matter such as this would normally have been handled by the attorneys, given that it was about the Russia investigation.

But the President's lawyer, Marc Kasowitz, who is designated to handle personal legal issues, was not traveling with the President and was largely uninvolved, according to the people familiar with the matter. The Times reported Wednesday that the President himself approved the statement, raising the possibility the President may have opened himself up to new legal issues not covered by attorney-client privilege. Jay Sekulow, the President's attorney, denied that Trump was involved.

"I wasn't involved in the statement drafting at all, nor was the President. I'm assuming that was between Mr. Donald Trump Jr., between Don Jr. and his lawyer. I'm sure his lawyer was involved, that's how you do it," said Sekulow in an interview on CNN's New Day.

Kasowitz's hiring was specifically intended to help shield White House aides from having to become witnesses in the ongoing investigation. As government employees, they aren't supposed to be involved in the President's personal matters.

The White House and lawyers for Kushner and Donald Trump Jr. did not comment for this story.

Multiple changing explanations for the meeting attributed to Donald Trump Jr. made a complex set of events spiral.

"It was a public relations disaster," one person close to Kushner's team told CNN.

Now, White House aides are pointing fingers at one another. Some of the discord is over a public relations strategy that seemed aimed in part at protecting Kushner, the only person in the June 2016 meeting who works in the White House and who already was under scrutiny for failing to disclose contacts with Russians. Donald Trump Jr., a private citizen, does not have an obligation to disclose the Russian meeting.

"Who do you have to protect? You have to protect the guy who filled out the form saying I never took this meeting," one of the sources said, referring to Kushner's SF-86 application for security clearance where meetings with foreigners need to be listed.

People close to the matter said that strategy went awry because Trump Jr. released misleading press statements.

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Two sources told CNN it was Kushner's team that discovered the emails showing Donald Trump Jr. accepted a meeting at Trump Tower with a lawyer who was presented as a Russian government lawyer able to provide damaging information about Hillary Clinton.

Kushner's lawyers were preparing documents to turn over to Senate Intelligence Committee investigators, and the email discovery created another problem for them.

Earlier this spring, Kushner had amended his SF-86 form submitted to the FBI as part of his security clearance application. At that time, in their second revision to the original form, the Kushner lawyers listed about 100 foreign contacts. But they did not list the June 2016 meeting with the Russian lawyer.

On June 21, Kushner's lawyers provided an amended SF-86 to the FBI, their third such change, to list the meeting with the Russian lawyer. Two days later, on June 23, Kushner met with the FBI to be interviewed for his security clearance.

On June 26, CNN asked a White House spokesman assigned to Kushner about the additional meeting on the amended security clearance form, including that it was organized by Donald Trump Jr.

But Kushner's team did not respond. On June 28, Jamie Gorelick, Kushner's lawyer handling the issue, sent a letter to the FBI to complain about what she believed was an improper leak, according to a person close to the matter.

The Kushner team also discussed whether they should immediately go public and disclose the meeting and the emails, given the press inquiry, according to a person close to Kushner. This person said Kushner knew of the newly discovered email by mid-June and told his lawyers he planned to sit down with the President to discuss the meeting and the email that had been discovered.

It's not clear what Kushner told the President. Trump told reporters Wednesday on Air Force One that he was not told the meeting was about obtaining dirt on Hillary Clinton.

The White House and Sekulow have said the President wasn't aware of the contents of the email until recent days, just before the Times published its stories beginning on Saturday.

The initial statement provided to the Times, and attributed to Donald Trump Jr., said the June 2016 meeting was about adoptions.

Even inside the White House and among other people involved in the process, there was discomfort because they knew the emails existed and they thought the statement was misleading.

The Times quickly followed up with a story showing that the Donald Trump Jr. knew the meeting was about negative information on Clinton.

Eventually, Trump Jr. published the emails himself, beating the Times to the punch after being notified by the paper that it was preparing to publish the emails.