Earlier this year, the US messaging platform had blocked access to the deleted items by a website called Politwoops, which collected deleted tweets from politicians in 30 countries.
At the time, Twitter claimed politicians had the same rights as other users to delete tweets after reflection, but on Thursday reversed its policy in the name of "holding public officials accountable."
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San Francisco-based Twitter said it reached an agreement with the Dutch-based Open State Foundation, which launched Politwoops in 2010, and the Sunlight Foundation, which monitors US politicians.
Politwoops, which began in the Netherlands and eventually spread to 30 countries, proved a frequent source of embarrassment for politicians, as well as a useful tool for journalists.
"Politwoops is an important tool for holding our public officials, including candidates and elected or appointed public officials, accountable for the statements they make, and we're glad that we've been able to reach an agreement with Twitter to bring it back online both in the US and internationally," said Jenn Topper of the Sunlight Foundation.
"In the coming days and weeks, we'll be working behind the scenes to get Politwoops up and running. Stay tuned for more."
Arjan El Fassed, director of the Open State Foundation, called the agreement "great news for those who believe that the world needs more transparency" and said plans are underway to expand to additional countries "to enable the public to hold public officials accountable for their public statements."
The agreement follows several meetings between Twitter with the Open State Foundation, Sunlight Foundation and digital rights organization Access Now.
In October, Twitter chief executive Jack Dorsey said the company had "a responsibility to continue to empower organizations that bring more transparency to public dialogue."
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