The UK Home Office says legal challenges against its plan to send some asylum seekers to Rwanda have not delayed the scheme.
But British media outlets quote campaigners as saying they received notice on Wednesday evening that the Rwanda flights will now not take place until at least after 6 June.
A Home Office spokesperson said: "The first flights are expected to take place in the coming months, legal action has not yet had any impact on this."
Prime Minister Boris Johnson had last week told the Daily Mail newspaper that he hoped the first flights would happen within a fortnight.
More people have been notified that they could be sent to Rwanda, the authorities say.
Under the £120m ($150m) scheme, people deemed to have entered the UK unlawfully will be transported to the East African country, where they will be allowed to apply for the right to settle.