The first flight due to take asylum seekers from the UK to Rwanda was cancelled minutes before take-off after legal rulings on Tuesday evening.
Up to seven people had been expected to be removed to the east African country.
But the flight was stopped after a late intervention from the European Court of Human Rights (ECtHR) led to fresh challenges in the UK courts.
Home Secretary Priti Patel said she was “disappointed” but added: “Preparation for the next flight begins now.”
However, James Wilson from campaign group Detention Action said the rare intervention from the ECtHR “shows how potentially dangerous” the Rwanda removals are.