Botswana cited immigration challenges, particularly in its neighbourhood, as the reason for refusing the request.
Sunak said the legislation would deter record numbers of migrants crossing the Channel from northern France, and disrupt people-smuggling gangs.
British PM Sunak promised on Monday to start sending asylum seekers to Rwanda within 10 to 12 weeks as the upper house of parliament finally passed the required legislation, delayed for weeks by attempts to alter the plan.
Britain's upper house of parliament rejected for a fourth time a piece of legislation needed to enable Prime Minister Rishi Sunak's plan to send asylum seekers to Rwanda.
The news delivers a major blow to Sunak, who has vowed to grow the economy as one of his top five priorities.
A majority of peers - 214 against 171 - voted to delay ratification of the treaty that London signed with Kigali.
The legislation would give UK ministers powers to disregard sections of international and British human rights legislation.
PM Rishi Sunak has staked his political future on slashing record levels of regular and irregular migration.
In his resignation letter to the prime minister, Jenrick wrote that the proposed laws were "a triumph of hope over experience".
During a bilateral meeting on Monday between President Hassan Sheikh Mohamud and UK Prime Minister Rishi Sunak
In a landmark diplomatic event, Prime Minister Rishi Sunak of the United Kingdom hosted a summit on Monday, November 20, welcoming Somalia's President Hassan Sheikh in London.
The UK Supreme Court rejected Wednesday a controversial government plan to send migrants to Rwanda and upheld a lower court ruling that it was unlawful, in a major setback for Prime Minister Rishi Sunak.