But Yolande Makolo, a spokeswoman for the east African state, did say Rwanda would be able to welcome more than 200 migrants initially.
The Prime Minister's plan to deal with asylum seekers arriving in the UK via irregular routes including the English Channel crossing is to place them on a one-way flight to Kigali.
He hopes this will deter other small boats attempting the journey from France.
Rwanda has entered into a five-year deal to take in migrants from the UK.
Asked by the BBC's Sunday With Laura Kuenssberg if Rwanda would be able to process tens of thousands of migrants as part of the deal, Ms Makolo said: "We will be able to welcome the migrants that the UK sends over the lifetime of this partnership.
"What I cannot tell you is how many thousands we are taking in the first year or the second year. This will depend on very many factors that are being worked out right now."
She had earlier claimed there was a "misconception" that Rwanda was only prepared to take 200 initial migrants, telling the BBC: "Journalists have been visiting the initial accommodation that we have secured since the beginning of the partnership. This is Hope Hostel.
"That particular facility is able to take up to 200 people.
"However, we have already started initial discussions with other facilities around Kigali and further afield and these will be firmed up and signed once we know how many migrants are coming and when they are coming.
"So it has never been the case that we can only take 200 initially, that has been a misconception."
Sir Keir Starmer has said Labour will not keep the Rwanda policy if it wins the next election, but this has prompted questions about what the party would do instead.
Ms Makolo urged critics of the plan not to attack Rwanda "unjustly", and to present a solution to the migrant crisis which was "not just deterrence and enforcement".
"People are suffering here so we need good solutions and we need to rethink the migration crisis," she said.
The spokeswoman later added: "Living in Rwanda is not a punishment. It is a beautiful country, including the weather."
Labour's national campaign co-ordinator Pat McFadden said if the party was in power it would spend the cash set aside for the Rwanda scheme on "a proper operation to crack down on the criminal gangs".
Mr McFadden said Labour believed the Government "will get flights off" but did not believe the scheme would provide "value for money for the taxpayer".
He also said he doubted Labour would work to return migrants to the UK from Rwanda should they form the next government.
Responding to Ms Makolo's comments, shadow home secretary Yvette Cooper said: "This interview shows that more people have arrived in the last week than are likely to be sent to Rwanda over the next few years, and the Conservatives are just trying to con people with their failing plans.
"Today, we heard a stark admission that Rwanda can only take a tiny proportion of people who are arriving in the UK, yet the Government is spending half a billion pounds of taxpayers' money on this scheme."
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