The legislation was unveiled on Tuesday.
"The current situation [with migrants] is neither moral nor sustainable. It cannot go on. It is completely unfair on the British people," the prime minister told a briefing aired on UK media, adding that the legislation "is tough, but it is necessary, and it is fair."
The prime minister said that "the number of people entering the UK illegally in small boats has more than quadrupled in just the last two years."
Sunak claimed that migrants arriving illegally to the UK were "not fleeing a war-torn country, prosecution, or an imminent threat to life," noting that the situation would get "worse and worse" if measures are not taken.
Migrants' illegal arrivals to the UK "will result in their detention and swift removal" within weeks "either to their own countries or to a safe third country like Rwanda," the prime minister said.
The UK and Rwanda signed a migration agreement in mid-April, stipulating that people recognized by the UK government as illegal migrants or asylum seekers will be deported to Rwanda for processing of documents, obtaining asylum, and relocation.
The first flight with illegal migrants aboard was scheduled for June 14, but it did not take place as the European Court of Human Rights granted a last-minute appeal to all the asylum seekers on board the day before. The court expressed fear that asylum seekers transferred to Rwanda would not have access to fair and efficient procedures for the determination of refugee status.