The Hotel Rwanda Rusesabagina Foundation said Mr Rusesabagina, a US permanent resident and Belgian citizen, has had no consular visits, and added that the Rwandan government’s claim that it had talked to his sons about a potential visit was “not true”.
The foundation added: “Paul’s wife has called the jail and has not been allowed to talk to him.”
His family said they believe he was “kidnapped” during a visit to Dubai, and that he would never knowingly have boarded a plane for Rwanda’s capital, Kigali.
Mr Rusesabagina has lived outside the East African nation since 1996.
He was awarded the US Presidential Medal of Freedom in 2005 for saving the lives of more than 1,200 people as a hotel manager during Rwanda’s 1994 genocide, in which some 800,000 Tutsis and moderate Hutus were killed.
Rwandan authorities have not responded to questions about how and where Mr Rusesabagina was apprehended, and have not publicly shared any international arrest warrant.
They have referred to “international cooperation”, but given no details.
“There is a deliberate effort to sanitise and present Rusesabagina as a victim,” the state-run Rwandan newspaper The New Times said in an editorial.
The paper rejected allegations he was arrested because of his criticism of the government.
Rwandan authorities have granted what they called an “exclusive” interview with Mr Rusesabagina to a Kenyan newspaper, The East African, in which he said he had been treated with “kindness” but did not discuss the accusations against him or how he was apprehended.
It is not clear when Mr Rusesabagina will appear in court.
Rwandan law says a suspect can be in provisional detention for 15 days, renewable for up to 90 days.
The Rwandan government has said it issued an arrest warrant for Mr Rusesabagina to answer charges of serious crimes including terrorism, arson, kidnap, and murder perpetrated against unarmed civilians.
Police called him the suspected “founder, leader, sponsor and member of violent, armed, extremist terror outfits including the Rwanda Movement for Democratic Change (MRCD)”.
Rwandan authorities point to a video posted online in 2018 in which Mr Rusesabagina says “it is imperative that in 2019 we speed up the liberation struggle of the Rwandan people … the time has come for us to use any means possible to bring about change in Rwanda, as all political means have been tried and failed”.
The MRCD has an armed wing, the National Liberation Front (NLF), that has been accused of attacks inside Rwanda in 2018 and 2019. Rwandan authorities arrested NLF spokesman Callixte Nsabimana last year.
Mr Rusesabagina in the past has denied the charges that he financially supports Rwandan rebels, saying he is being targeted for criticising the administration of President Paul Kagame over human rights abuses.
His detention has prompted concern among human rights activists that this was the latest example of the Rwandan government targeting critics beyond its borders.
The US government has said it expects the Rwandan government to provide “humane treatment, adhere to the rule of law and provide a fair and transparent legal process” for Mr Rusesabagina.