Zimbabwe authorities have said that O'Donovan was the one who wrote them because they came from her IP address.
The 25-year-old New Jersey native is accused of calling the 93-year-old President of Zimbabwe, Robert Mugabe, a "selfish & sick man" in a Twitter post, showing him with a catheter.
The AP also reports that the Zimbabwe Lawyers for Human Rights say they have represented almost 200 charged for allegedly insulting the Zimbabwe president in recent years. The account was active on Friday and Saturday even though O'Donovan is in custody. She could face 20 years in prison because of that.
O'Donovan is also charged with undermining or insulting the authority of the president.
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Two men were arrested separately on Friday after they allegedly said "I will not vote ZANU-PF and president Mugabe is like a dog", referring to the ruling party.
O'Donovan has denied the allegations as "baseless and malicious".
"Mugabe... created the cyber-security ministry as an attempt to clamp down on social media movements that pose a big threat to his regime ahead of the election", Bulawayo-based analyst Dumisani Mpofu previously told AFP. Zimbabwe was shaken previous year by the biggest anti-government protests in a decade.
Martha O'Donovan works for Magamba TV, a local company that specialises in political satire. Earlier this year, she presented a talk at a digital culture conference on "How Zimbabweans Rebel Online".
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The group representing Ms O'Donovan, Zimbabwe Lawyers for Human Rights, says it has represented almost 200 people charged for allegedly insulting Mr Mugabe, the world's oldest head of state, in recent years.
"This arrest marks the start of a sinister new chapter in the Zimbabwean government's clampdown on freedom of speech, and the new battleground is social media", the Amnesty statement read in part.
But I must admit, I do respect Martha O'Donovan's gangster.
"The reported offensive and insulting tweet does not make any mention of the president's name", Zimbabwe Lawyers for Human Rights (ZLHR) said in a statement.
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