They get to, quote, fact-check that president of the United States, in an untruthful way, not fact check Chinese propaganda until we pointed out and they started doing it moments ago, but yet we don't get to ask who the fact-checkers are?' she said.
Mr Trump wrote a similar post on Facebook post about mail-in ballots on Tuesday, and no such warnings were applied.
Trump earlier this week tweeted there was "no way" mail-in ballots would be "anything less than fraudulent" - although both Trump and McEnany have voted absentee.
House Speaker Nancy Pelosi said it was "outrageous" that while Twitter had put a fact-check tag on Trump's tweets asserting massive mail-in election fraud, it had not removed his tweets suggesting without evidence that a TV news host had murdered an aide years ago. He has warned repeatedly that expanded voting by mail will lead to widespread voter fraud.
According to a Twitter spokesperson, the company made a decision to apply the fact-checks on Trump's tweets about the mail-in ballots because they contain "potentially misleading information about voting processes".
However, the president cannot unilaterally regulate or close the companies, and any effort would likely require action by Congress. "And we will admit to and own any mistakes we make", tweeted Dorsey.
"This proposed executive order seems created to punish a handful of companies for perceived slights", said Jon Berroya, chief executive of the Internet Association, a lobbying group representing numerous major tech companies.
Trump criticizes two states for advancing vote-by-mail options
There's a fight playing out in both state and federal courts about just who is eligible to vote by mail in Texas. The president also took to Twitter twice on Sunday to blast moves to make it easier to vote by mail in November.
Twitter has said it will decide internally when to use a label, and on which tweets, and will draw from information curated from news outlets.
Separately, a three-judge panel of the US Court of Appeals in Washington on Wednesday upheld the dismissal of a lawsuit by a conservative group and right-wing YouTube personality against Google, Facebook, Twitter and Apple accusing them of conspiring to suppress conservative political views.
He tweeted to his more than 80 million followers that Republicans felt the platforms "totally silence conservatives" and that he would not allow this to happen. It's up to the user to click on the button to understand more.
Republican Senator Josh Hawley, a frequent critic of Big Tech companies, sent a letter to Mr Dorsey asking why Twitter should continue to receive legal immunity after "choosing to editorialise on President Trump's tweets".
Donald Trump has recently doubled down on unsupported claims that former Rep. Joe Scarborough was involved in the 2001 death of his staffer, which was ruled accidental by authorities. According to medical examiners, Klausutis died from an undiagnosed heart problem.
Social media company Twitter has always been Trump's soapbox - his direct voice to the people, he claims.
"We are deeply sorry about the pain these statements, and the attention they are drawing, are causing the family", a Twitter spokesperson said. "We've been working to expand existing product features and policies, like the labels you're seeing today, so we can more effectively address things like this going forward".