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Badawi family's spokesperson, Dr Elham Manea, who is also an associate professor specialising in the Middle East at University of Zurich, said on Facebook that the news was delivered by a Saudi ambassador in Germany.
She wrote: "Saudi ambassador in Germany informed NDR-TV that flogging will not continue and #RaifBadawi maybe not have to serve the whole time in prison."
The announcement came as Badawi's second round of lashing, due to take place on Friday (23 January), was postponed for the second time due to his deteriorated health.
Badawi was publicly flogged 50 times after prayers on Friday (9 January) and was set to be lashed every week for the next 19 weeks until the punishment was complete.
However, the second round of flogging was postponed as doctors concluded his wounds had not yet healed properly.
Badawi was arrested in 2012 for encouraging free speech on his blog, which has since been closed. He was accused of "setting up a website that undermines general security" and "ridiculing Islamic religious figures".
'No freedom of expression in Saudi Arabia'
Hundreds of people around the world are protesting against Badawi's punishment.
Amnesty International, which has been advocating for the release of Badawi, has been organising vigils in many countries in the world.
One of the protests took place outside the Saudi Embassy in London on Thursday (22 January).
Speaking to IBTimes UK, director of Amnesty UK Kate Allen said: "The world should be shocked and horrified by what's happening in Saudi Arabia.
"The flogging is going to happen as long as Badawi's health holds up. We are campaigning worldwide, to have this flogging stopped and to have him freed from prison. Because he is a prisoner of conscience.
"We will continue to campaign and we need to make sure that the international community raises its voice.
"There is no freedom of expression in Saudi Arabia, where the government uses torture and death penalty in a shocking way and human rights are not observed."