Two Rwandan exiles living in London were warned last week by UK police that they faced the threat of assassination.
It has emerged that the men were visited by officers who told them they were in danger of being killed by a hitman sent by the Rwandan government.
Shortly before the warning was issued, a Rwandan man suspected of involvement was prevented from entering the UK.
The Rwandan High Commission in London has denied involvement in any alleged plot to kill the two exiles.
"The government of Rwanda does not threaten the lives of its citizens wherever they live," High Commissioner Ernest Rwamucyo said.
The government later said that the Metropolitan police had not approached it with evidence of the allegations.
"We are ready as always to work with them to ensure that nobody, be they Rwandan or not, is the victim of violence on British soil", a statement said, quoted by the New Times website in Kigali.
The two men - Rene Mugenzi and Jonathan Musonera - have both been involved in political groups opposed to the ruling party of Rwanda's President Paul Kagame.
A week ago, UK police officers knocked on their doors and told them that they could not guarantee their safety. They advised them to increase the security around their homes or move away.
The police gave them written statements saying: "The Rwandan government poses an immediate threat to your life. The threat could come in any form."
It is understood that shortly before visiting the two men, counter-terrorism officers had stopped a Rwandan man as he tried to enter the country at Folkestone.
They questioned the unidentified man and turned him away.
Mr Musonera said he and his family were very scared.
"I was not surprised, because this is not the first time they've tried to disturb the opposition," he told the BBC's Focus on Africa programme after learning about the death threat.
"I take this problem very seriously. I used to drive my car. Right now I stopped because the police told me to use limited movement or go out with friends.
"My wife, she is scared. We have cut off the home phone. The children now they stay at home, they can't go out. They can't go out with friends. I stopped visitors coming to our home."
BBC Africa analyst Martin Plaut says it is not the first time there have been reports of threats to Rwandan exiles living in the UK.
The UK's Security Service (MI5) has apparently been attempting to prevent an assassination campaign for some time, he adds.
In April, it was reported that MI5 had warned Mr Rwamucyo to halt an alleged campaign of harassment against critics of his country's government.
The police's warning was issued just prior to a meeting in London of exiles last weekend that brought together Tutsi and Hutu opposition politicians.
The meeting heard from a former Rwandan chief of staff, Lt Gen Faustin Kayumba Nyamwasa, who addressed the gathering by videolink from South Africa, where he survived an assassination attempt in June 2010.
The Rwanda government has denied any links to the shooting of Gen Nyamwasa, who was a close ally of Mr Kagame before fleeing to South Africa last year.
The party representing the imprisoned Hutu politician, Victoire Ingabire, was also at the meeting.
The possibility that Hutu and Tutsi political parties could begin working together would be worrying for the Rwandan government, our correspondent says.
In January, four former top officials - including Gen Nyamwasa - who have fallen out with Mr Kagame and gone into exile were sentenced in absentia to long terms in prison for threatening state security and promoting ethnic divisions.
President Kagame's Rwandan Patriotic Front came to power in 1994, ending the genocide in which some 800,000 ethnic Tutsis and moderate Hutus were killed.
He was re-elected last year with 93% of the vote, amid opposition claims of harassment.