No asylum seekers have yet been sent to the African country, with Mr Sunak insistent that his legislation will help the first deportation flights get off the ground.
So far the UK has sent £240m to the east African nation, with another £50m payment scheduled in the coming year.
Just £20m of the money allocated so far has gone toward set-up costs, including accomodation for asylum seekers who arrive, with the remainder penned for investment in “economic transformation”.
Labour has warned the scheme could cost £400m based on the cost of supporting each asylum seeker in Rwanda once they arrive.
Assked by the BBC, on the sidelines of the World Economic Forum in Davos, why his country was taking millions of pounds of UK money without taking any asylum seekers, Mr Kagame replied: “It’s only going to be used if those people will come.”
The Rwanda president added: “If they don’t come, we can return the money.”
Mr Kagame did not clarify how much of the money he would return, or when. Asked by the BBC about the current political and legal obstacles around the deal with his country, Kagame said: “Ask the UK – it is the UK’s problem, not Rwanda’s problem”, he said.
Labour’s Yvette Cooper has said the government should “seize the chance” to get money back from Rwanda after Paul Kagame’s offer of a refund.
“If Rwanda says we can have the money back from this failing scheme, Rishi Sunak should seize the chance, instead of dragging out this Tory asylum chaos any longer. We need proper grip not more of this failing gimmick,” said the shadow home secretary.
Although Mr Kagame’s comments at Davos appeared offhand, a top official later confirmed Kigali would listen to requests for a refund.
Yolande Makolo, the Rwandan government’s spokesperson, said: “Under the terms of the agreement, Rwanda has no obligation to return any of the funds paid.”
“However, if no migrants come to Rwanda under the scheme, and the UK government wishes to request a refund of the portion of the funding allocated to support the migrants, we will consider this request.”
Labour’s Stephen Kinnock pointed to the Home Office’s impact assessment – which revealed the plan would cost the government £169,000 per asylum seeker sent to Rwanda.
The shadow immigration minister told the Commons: “This whole sorry tale is a shambolic farce, and the cost to the taxpayer of the Rwanda policy, of the this legislation and of the asylum backlog, has become utterly extortionate.”
Mr Sunak faces his biggest personal crisis as prime minister tonight as he faces a showdown vote to get his Rwanda bill through parliament.
A group of 60 right-wing Tory MPs threatened the PM’s deportation legislation by backing amendments aimed at toughening it up on Tuesday evening.
Lee Anderson and Brendan Clarke-Smith quit as deputy chairmen after siding with rebels. Ex-immigration minister Robert Jenrick and others have said they are willing to defy the government later on Wednesday.
If around 30 of the rebels carry out their threat, Mr Sunak will be handed a humiliating defeated – potentially sparking yet another Tory leadership contest or a general election within weeks.
No 10 offered fresh concessions to the Tory right-wing rebels, as illegal migration minister Michael Tomlinson said ministers were considering tweaking the civil service code to remind officials to follow ministerial decisions.
It comes amid concerns by Tory rebels that the Rwanda legislation fails to go far enough to block last-minute, rule 39 injunctions from the European Court of Human Rights (ECHR).
But one senior Tory rebel told The Independent they were “not particularly impressed” by the assurance the code would be tweaked.
A close ally of Mr Sunak has said most of the Tory rebels will “wimp out” when it comes to Wednesday evening’s crucial vote.
The senior Conservative MP told The Independent: “They will wimp out at the third reading. They’ll fall into line. Voting against the bill would force a general election now – so why would they do it?”
Another Tory MP loyal to Mr Sunak said: “Most realise to defeat the government to bring down one of its major policies on this would be political madness.”