President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE blasted so-called White House “leakers” as “traitors” and vowed to hunt them down, even as he denied the West Wing has a problem with leaks.

“The so-called leaks coming out of the White House are a massive over exaggeration put out by the Fake News Media in order to make us look as bad as possible,” Trump tweeted Monday afternoon.

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The president, however, indicated an investigation is underway into who in the White House is sharing information with the press.

“With that being said, leakers are traitors and cowards, and we will find out who they are!” he wrote.

The so-called leaks coming out of the White House are a massive over exaggeration put out by the Fake News Media in order to make us look as bad as possible. With that being said, leakers are traitors and cowards, and we will find out who they are! — Donald J. Trump (@realDonaldTrump) May 14, 2018

The comments come days after The Hill first reported that White House aide Kelly Sadler made off-color comments about Sen. John McCain John Sidney McCainCindy McCain endorses Biden: He's only candidate 'who stands up for our values' Biden says Cindy McCain will endorse him Biden's six best bets in 2016 Trump states MORE’s (R-Ariz.) cancer diagnosis.

Sadler said during an internal meeting that McCain’s opposition to CIA director nominee Gina Haspel “doesn’t matter” because “he’s dying anyway,” according to sources familiar with her comments.

The White House has refused to offer a public apology for the remarks and Trump’s response is almost certain to further fuel the controversy surrounding them.

Lawmakers on Capitol Hill and members of McCain’s family ramped up their calls for Sadler to apologize publicly for her comments.

Senate Majority Whip John Cornyn John CornynThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight Senate GOP faces pivotal moment on pick for Supreme Court MORE (R-Texas) told reporters Monday “an apology is appropriate ... from the person who said that really dumb thing.”

Sen. John Thune John Randolph ThuneSenate GOP sees early Supreme Court vote as political booster shot Romney backs pre-election Supreme Court vote, paving way for McConnell, Trump Senate GOP faces pivotal moment on pick for Supreme Court MORE (S.D.), the Senate's No. 3 Republican, criticized the White House's response, saying it has worsened the situation.

"It's just a really unfortunate circumstance," Thune said. "Obviously what was said was very wrong and inappropriate. It would have been a lot easier if they had just nipped it right away ... Now it's [dragged] on for five days."

White House spokesman Raj Shah suggested no apology would be forthcoming, saying the matter is “being addressed internally."

Shah and the communications staff have focused more on how Sadler’s comments became public than on the nature of the remarks themselves — a concern echoed by Trump.

"If you aren’t able, in internal meetings, to speak your mind or convey thoughts or say anything that you feel without feeling like your colleagues will betray you, that creates a very difficult work environment," Shah said.

Trump weighed in on the news reports minutes before he took off in Marine One to visit first lady Melania Trump Melania TrumpMelania Trump: Ginsburg's 'spirit will live on in all she has inspired' The Hill's 12:30 Report - Presented by Facebook - You might want to download TikTok now Warning label added to Trump tweet over potential mail-in voting disinformation MORE at Walter Reed National Military Medical Center, where she underwent a kidney procedure earlier in the day.

Jordain Carney contributed. Updated at 5:43 p.m.