Badawi, now 33, co-founded a discussion group called the Saudi Liberal Network Internet.
He was arrested in June 2012 under cyber crime provisions, and a judge ordered the website shut after it criticised Saudi Arabia's notorious religious police.
Badawi was sentenced in 2014 to 1,000 lashes and 10 years in prison in a case that triggered international outrage.
"It's not fair that our father is in prison. He's not killed anybody. He just created a blog. It's not illegal," one of his two daughters, Najwa, said in a video released by Amnesty International.
Sister of jailed Saudi blogger imprisoned: NGO
Badawi's wife Ensaf Haidar and their three children, aged 14, 10 and eight, have lived in Quebec, Canada since 2013.
Supporters around the province and in Montreal held rallies to call for Badawi's release.
The Quebec government reiterated its support for Badawi and said it would keep working to secure his release.
The European Parliament gave Badawi its Sakharov Prize for freedom of expression in 2015.
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