Zimbabwe's main opposition party says a military coup would not help solve the country's many problems.
Mr Tatchell says members of the defence forces are plotting against Mugabe
British gay rights campaigner Peter Tatchell claims a new armed group of soldiers and police officers has been formed to topple Mr Mugabe.
But a spokesman for the opposition Movement for Democratic Change says he "is not aware" of any attempt to use force against President Robert Mugabe.
Mr Mugabe is accused of rigging elections and ruining the economy.
He blames Zimbabwe's problems on a Western plot to stop him seizing white-owned land.
Meanwhile, a Harare court has rejected an appeal by directors of the banned Daily News to have criminal charges against them dropped and so they should stand trial.
Mr Tatchell has twice tried to perform a citizen's arrest on Mr Mugabe for alleged human rights abuses.
He says that he is not involved in the Zimbabwe Freedom Movement (ZFM) but is merely releasing a statement and video recording on behalf of a group of members of the Zimbabwe defence forces and police.
"If Mugabe refuses to go, the ZFM will remove him and his cronies by force," reads a statement signed by national commander Charles Black Mamba and deputy national commanders Ntuthuko Fezela and Daniel Ingwe.
Mr Tatchell said the ZFM was being formed because "all opportunities and possibilities for peaceful democratic change have been closed down".
However the video and images shown by Mr Tatchell could have been recorded anywhere and no evidence was given that this movement really does exist.
Ruling Zanu-PF party spokesman Nathan Shamuyarira in Harare told the BBC he did not wish to comment because he said he did not want to give credibility to a story that was entirely groundless.
It later emerged that the group has made contact with the British High Commission in Harare, looking for support.
A foreign office minister told journalists he believed one or more members of the group had made what he described as an informal approach, but had been told - very firmly - that the British government could have nothing to do with any attempt to overthrow the government of Zimbabwe by force.
BBC Africa analyst Liz Blunt says that even the remotest suggestion of disaffection in the armed forces is likely to increase government pressure on Zimbabwe's opposition.
MDC spokesman Paul Themba Nyathi, who has been charged with treason after helping to organise a national strike against the government earlier this year, said a coup was not the answer.
He told BBC News Online: "I don't think a military coup would be helpful.
"We are staging a struggle through lawful means, even in a restrictive environment."
He said he did not know of any military unrest in Zimbabwe, but added that soldiers were suffering the same hardships as other Zimbabweans.
Inflation is running at more than 455% and up to half the population needs food aid.
Mr Nyathi said the solution was for Zimbabwe's neighbours to put pressure on Mr Mugabe to hold new elections, which would be "free and fair".
On Wednesday, a South African-based newspaper, This Day, released a special edition in Harare urging Mr Mugabe to step down.
It also condemned the South African Government for its "shameful silence" on the crisis in Zimbabwe.