Zimbabwean police have charged an American citizen with a new offence of plotting to overthrow a constitutionally elected government, her lawyer has said.

Martha O’Donovan had earlier been charged over a tweet that appeared to insult Robert Mugabe, weeks after the president appointed a cybersecurity minister to police social media.

O’Donovan was detained on Friday morning, a US embassy spokesman told the Associated Press. Her lawyer, Obey Shava, said she faced two charges – undermining the authority of or insulting the president and plotting to overthrow the government - of tweets that police claimed were “emanating from her IT address”The exact words of the insult are unclear. Shava said his client had been accused of tweeting “We are being led by a selfish and sick man” from the Twitter handle @matigary.

The tweet had a photo illustration of the 93-year-old Mugabe with a catheter, according to the police charge sheet.

However, Zimbabwe Lawyers for Human Rights, an activist group, said the offending tweet referred to a “goblin whose wife and stepson bought a Rolls-Royce”.

The tweet did not refer to Mugabe by name, ZLHR said, but Russell Goreraza, who is Mugabe’s stepson with his wife, Grace, is thought to be the only individual to have recently imported two Rolls-Royce vehicles into the country.

The British-built cars, both Rolls-Royce Ghosts that sell for about $220,000 (£170,000) and have a top speed of 155mph, are marketed by the manufacturer as “more measured, more realistic” than the $300,000 Rolls-Royce Phantom.

Goreraza is also reported to have purchased two Range Rover 4x4s, two Mercedes-Benz S-Class limousines and an Aston Martin, while Grace Mugabe is also thought to have acquired a Rolls-Royce.

Footage of Goreraza taking delivery of the vehicles prompted outrage when it was circulated on social media last month.

“I deny the allegations levelled against me as baseless and malicious,” O’Donovan said in a signed statement shown to Associated Press.

The ZLHR said police had transferred O’Donovan, who works for the Harare-based Magamba TV, to the city’s central police station and confiscated her laptop. Police in Harare did not respond to calls for comment.

There have been several arrests in recent years for actions deemed to undermine the president, although no one has ever been convicted.

Last year, ministers told Zimbabweans that statements posted on social media could be traced and might lead to punishment.

A new wave of activists have used social media to organise protests against Mugabe’s rule. One of the most effective was the #ThisFlag movement last year which was organised by the pastor Evan Mawarire.

George Charamba, a government spokesman, said in October that Mugabe had created the new ministerial post to deal with an “emerging threat to the state … a threat founded on abuse and unlawful conduct”.

O’Donovan had been working with social media outlet Magamba TV, which has a cult following among educated, urban youth in Zimbabwe.

The outlet describes itself as producing “satirical comedy sensations”. O’Donovan, a graduate of New York University, has called herself a manager for Magamba TV and a media activist. Earlier this year, she presented a talk at a re:publica digital culture conference titled “How Zimbabweans Rebel Online”.

O’Donovan was employed at Magamba TV as a ‘project officer’ and has no link to the twitter feeds cited by the police, associates said. Authorities have made a series of attempts to intimidate the network.

Tensions are rising in Zimbabwe as the economy deteriorates and a vicious struggle to succeed Mugabe, who has been in power for more than 35 years, intensifies. The main contenders to take power when the president steps down or dies are his wife and Emerson Mnangagwa, a vice-president who has significant support within the security establishment.

The first lady is unpopular with Zimbabweans, who have been incensed by reports of her extravagant spending, and has shown herself to be sensitive to criticism. Last month, a Zimbabwean journalist who reported that she donated used clothing, including underwear, to supporters of the ruling Zanu-PF party was charged with causing a criminal nuisance. The first lady was accused of assaulting a girlfriend of one of her sons in a luxury apartment in South Africa earlier this year.

Two men were arrested separately on Friday after they allegedly said: “I will not vote Zanu-PF and President Mugabe is like a dog”.

ZLHR says it has represented almost 200 people charged with allegedly insulting world’s oldest head of state in recent years.

Mugabe has already been named by Zanu-PF as its presidential candidate for the 2018 elections.