According to Vijaya Gadde, a Legal, Policy and Trust & Safety Lead at Twitter, the move has triggered "significant feedback" from the users over the past 24 hours, "from critical to supportive".
"After reflecting on this feedback, we have decided to make changes to the policy and how we enforce it," Gadde said on her account.
In a tweet within the same thread, she listed the changes as the following: "1. We will no longer remove hacked content unless it is directly shared by hackers or those acting in concert with them. 2. We will label Tweets to provide context instead of blocking links from being shared on Twitter."
The rest of the distribution rules of hacked materials will remain in place, the company official added.
Twitter Vice President for Global Communications Brandon Borrman, in turn, told CNBC channel that the links to the New York Post would still remain blocked as they contain images with email addresses and phone numbers which count as personal information.
On Thursday, Twitter limited the display of links to a New York Post article about the son of US presidential candidate Joe Biden, Hunter, saying that it did not want to let its platform be used for distributing content obtained without authorization. A storm of comments under the announcement as well as statements by numerous public figures that followed suggest many considered the step an act of censorship.
The article by the New York Post contained two emails that Hunter Biden had purportedly received from a top official at Ukrainian energy company Burisma when he was its employee. In the May 2014 email, Burisma board adviser Vadym Pozharskyi asked Hunter Biden to "use [his] influence" to support the Ukrainian company politically. In another email, dated April 2015, he thanked Biden Jr. for arranging a meeting with his father for him.
The emails were allegedly sourced from the hard drive of Hunter Biden's damaged personal laptop that was dropped off for repairs at a local store in his home state of Delaware. If proven to be authentic, they would challenge Joe Biden's campaign claims that he had never had anything to do with his son's business dealings.