Mr Sunak posed for photos with Paul Kagame at Downing Street before welcoming him into the building for talks.
The discussion with Mr Kagame is part of a host of bilateral meetings Mr Sunak is holding as world leaders and their representatives descend on London for the king’s coronation on Saturday.
The UK has agreed a multimillion-pound partnership with Rwanda designed to tackle the number of small migrant boats sailing to Britain on unauthorised routes.
The £140 million ($176 million) deal will see some migrants who enter unlawfully by the English Channel sent to Kigali if they cannot be deported to their home country.
“Rwanda and the UK are great friends and we have demonstrated that with our migration and economic partnership, which I think shows us leading the way in finding global solutions for shared international challenges,” Mr Sunak said, opening the discussions in No 10’s pillared room.
The Conservative Party leader also praised Mr Kagame’s role as chair-in-office of the Commonwealth over the past year, saying he had “led the way” on issues such as trade and sustainability.
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Mr Kagame said he was “grateful” for the partnership between London and Kigali.
The plan to send migrants to Rwanda — a policy ruled lawful by High Court judges — has so far been stalled by legal action and no flights have taken off.
It is part of wider proposals to deter unlawful migration, including housing refugees in barges off the English coast while their asylum claims are processed.
Later in their conversation, Mr Sunak expressed his “sympathies” for the flooding in Rwanda, which has left at least 129 people dead.
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The British leader also spoke to the prime minister of Spain, Pedro Sanchez, over the phone on Thursday.
According to Downing Street, the pair “welcomed the strong and growing economic, security and cultural ties between the UK and Spain, as well as wider co-operation with European partners”.
“On Gibraltar, the leaders agreed on the importance of progressing negotiations on a UK-EU treaty and concluding a suitable agreement as soon as possible," the Downing Street spokesman said.
“They also discussed the situation in Ukraine and reaffirmed the UK and Spain’s enduring support for Ukraine’s defence against Russia’s illegal invasion and [Ukrainian] President [Volodymyr] Zelenskyy’s plan for peace.”
Mr Sunak is expected to meet more leaders on Friday.