Election watchdog the Electoral Commission issued a warning calling on all parties and candidates to respect "transparency and integrity" during the campaign, after the party's verified press office account was temporarily renamed "factcheckUK".
The move has been widely criticised as something that could have misled the watching public.
Twitter issued a sharp rebuke that "any further attempts to mislead people" would result in "decisive corrective action"
A spokesman for the Electoral Commission said: "Voters are entitled to transparency and integrity from campaigners in the lead-up to an election, so they have the information they need to decide for themselves how to vote.
"The Electoral Commission seeks to deliver transparency to the public through the political finance rules.
"While we do not have a role in regulating election campaign content, we repeat our call to all campaigners to undertake their vital role responsibly and to support campaigning transparency."
Opposition parties accused the Tories of adopting the tactics of Donald Trump or Vladimir Putin to deliberately mislead the public.
However Foreign secretary Dominic Raab has sought to downplay the incident, saying "no one gives a toss about the social media cut-and-thrust".
But Twitter told the Conservative Party that any further attempts to "mislead people" during the UK election will result in action.
"Twitter is committed to facilitating healthy debate throughout the UK general election," it said in a statement.
"We have global rules in place that prohibit behaviour that can mislead people, including those with verified accounts.
"Any further attempts to mislead people by editing verified profile information - in a manner seen during the UK Election Debate - will result in decisive corrective action."
The Conservative Campaign Headquarters press office account was renamed “factcheckUK” during Tuesday evening’s ITV broadcast, offering commentary on Labour leader Jeremy Corbyn’s statements and retweeting messages supporting Boris Johnson.
The move was criticised by independent fact-checking charity Full Fact, which tweeted: “It is inappropriate and misleading for the Conservative press office to rename their twitter account ‘factcheckUK’ during this debate. Please do not mistake it for an independent fact checking service such as @FullFact, @FactCheck or @FactCheckNI.”
The @CCHQpress account is verified by Twitter, displaying a blue tick which is intended to denote that a user is genuine.
The Liberal Democrat press office posted an image suggesting they were reporting the account to Twitter for “pretending to be me or someone else”.
They tweeted: “And people wonder why trust in politics has been eroded @CCHQPress”
Liberal Democrat Brexit spokesman Tom Brake said: "This is straight out of Donald Trump or Putin's playbook.
"Not content with excluding the voice of Remain from this debate, the Tories are now resorting to deliberately misleading the public.
"People know they can't trust a word that Boris Johnson or the Conservatives say."
Shadow women and equalities secretary Dawn Butler said social media firms must "do better".
Speaking to ITV News, she said the Tories think "this is a game, they think it's a laugh, they don't really care".
"Twitter issued the equivalent of a written warning, which is just crazy - we know what social media is about," she said.
"We know how quick it is for fake news to dominate. And so Twitter could have done something a lot sooner.
"They could have put the account back to its original status, they could have removed the blue tick - if they want to punish them, they should remove the blue tick because it's not a legitimate site when you are impersonating another site.
"Or they could have taken it down. If they want to act quickly, they should have just taken it down."
Labour’s David Lammy tweeted: “The Conservative Party press office @CCHQPress rebranding themselves as ‘FactCheckUK’ shows what disdain this party and this government has for the truth.”
“The Electoral Commission must investigate and punish this blatant attempt to decieve the public.”
Meanwhile, some other Twitter users also changed their display names to factcheckUK and posted critical comments about Mr Johnson.
Others changed their display name CCHQ Press Office, while Tony Blair’s former spokesperson Alastair Campbell changed his display name to Boris Johnson and tweeted: “I won’t get Brexit done #FactCheck”
Foreign Secretary Dominic Raab said the party make "no apologies" for the party's Twitter account rebrand.
He said: "We make no apologies for rebutting the nonsense that's put around.
"In every election it's done and perhaps in the past we haven't been hot enough on picking up on those lies and nailing them and we're not going to see that happen this time and this is about rebutting the nonsense with factual answers about what the Conservatives stand for."
He went on to welcome Twitter's warning, adding: "We'll always take advice from Twitter and the like but the reality is we're going to continue to rebut, in as forceful way as we can, the nonsense and the lies put around by Jeremy Corbyn particularly on the NHS which is not just safe under the Conservatives but will go from strength to strength."
The row comes amid repeated accusations that Mr Johnson struggles to tell the truth.
The Prime Minister was met with derisive laughter from the ITV studio audience in Salford on Tuesday night when he said that he considered the truth was "very important" in the General Election.