As reported on the BBC News website:
It comes after new board member, Tesla boss Elon Musk, asked his followers in a Twitter poll whether they wanted the feature.
Many users have long called for an edit button but there are concerns about how to execute it.
Twitter said it would start testing the idea in the coming months.
The social media firm's communications team tweeted: "Now that everyone is asking… yes, we've been working on an edit feature since last year!
"No, we didn't get the idea from a poll," it added.
"We're kicking off testing within @TwitterBlue Labs in the coming months to learn what works, what doesn't, and what's possible."
Users of Twitter Blue, the platform's subscription service, get early access to features it is testing.
Under an edit function users could be able to fix typos or errors in a tweet without losing any replies, retweets or likes it has already gained.
Jay Sullivan, the company's vice president of consumer product, said it had been "the most requested Twitter feature for many years" in a thread on Tuesday.
However, he said the company was exploring how to build the feature "in a safe manner".
"Without things like time limits, controls, and transparency about what has been edited, Edit could be misused to alter the record of the public conversation," he said. "Protecting the integrity of that public conversation is our top priority when we approach this work."
During a talk in 2018, former Twitter boss Jack Dorsey said the firm would "probably never" add the feature amid concerns about transparency.
But rival social media platforms Facebook and Instagram already allow users to edit their posts, and Twitter's new boss Parag Agrawal appears open to the idea.
Elon Musk started a poll on Monday after disclosing that he owned a 9.2% stake in Twitter, which made him the firm's biggest shareholder.
On Tuesday it was announced that he had been appointed to Twitter's board.
The poll has already attracted over four million votes.
Twitter initially said it was exploring an edit button on 1 April but it was widely interpreted as an April Fool's joke.
Twitter says it was already working on an edit button before Elon Musk was appointed to its board.
But it does certainly look like the Tesla boss has moved the process along.
Twitter polls are notoriously unscientific - yet Mr Musk appears to make real-life decisions based on their results.
In November last year, he asked his 80 million followers whether he should sell 10% of his Tesla stock. The poll concluded he should, and he did.
Mr Musk's poll on whether there should be an edit button on Twitter is being taken seriously by the chief executive of Twitter. "The consequences of this poll will be important. Please vote carefully," Parag Agrawal said.
It certainly suggests that Twitter will now look to change its policy in this area as a consequence of the poll result.
Mr Musk overnight has generated huge influence over Twitter - and he seems to be giving his followers the ability to choose what approach he takes.
This was day one remember, who knows what else he might do in this new powerful position.
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