US Representative Ilhan Omar has condemned a Republican state senator from North Dakota who posted a long-debunked photo on his Facebook page that purports to show the Minnesota Democrat holding a weapon at an al-Qaeda training camp.

Omar, a naturalised US citizen who was born in Somalia and is one of the first Muslim women elected to Congress, blasted state Senator Oley Larsen’s post, which also led to calls Tuesday from the Senate’s top Republican and GOP Governor Doug Burgum to apologise and relinquish a state Senate leadership position.

“This is pure propaganda designed to stir up hate and violence,” Omar tweeted Monday night. “Facebook’s unwillingness to crack down on hate speech and misinformation is not just threatening my life, but our democracy.”

The image Larsen posted has been debunked by several sources since it appeared on social media this summer. It is an Associated Press photo taken of a female Somali army recruit at a Mogadishu military training campus in 1978, four years before Omar was born in 1982.

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In the comments accompanying his post, Larsen also called Omar an “elected terrorist” and asked his followers to “share it everywhere.”

Facing mounting criticism, though, Larsen removed the photo Monday. And by Tuesday morning, his Facebook feed – minus the image – was full of attacks on him for posting it and accusing him of bigotry.

On Tuesday, the North Dakota Senate’s majority leader, Republican Rich Wardner, called on Larsen to apologise and give up his position as the state Senate’s president pro tempore, a post in which he presides over sessions when the lieutenant governor is absent.

“At this point, I’m not calling for his resignation from the Senate, but if he continues with this, I will have to rethink that,” Wardner said.

The governor’s spokesman, Mike Nowatzki, said: “The governor supports the actions requested by the majority leader.”

Neither Larsen, who is from Minot, nor Facebook responded to requests for comment.

Facebook has been under fire from politicians, regulators and privacy advocates around the world over problems ranging from election security to what many consider its disproportionate, often negative influence on society.

While Facebook has said it is stepping up efforts to remove content that violates its rules, it has also said it is not the company’s role to fact-check or judge the veracity of what politicians say.