Both of the candidates looking to succeed Boris Johnson say they back — and would even expand — the ousted prime minister’s controversial plan to send illegal immigrants in large numbers to the African nation of Rwanda, a plan sharply denounced by immigrant and human rights groups in the U.K.

Rishi Sunak, Mr. Johnson’s former chancellor of the exchequer and the son of African-born parents of Indian descent, and rival Liz Truss, the foreign secretary, made clear they back the Rwanda plan as they face a vote of Conservative Party members nationwide to replace the scandal-plagued Mr. Johnson. 

A new prime minister is expected to be named by early September and British political handicappers say the race is tight.

Mr. Sunak vowed to do “whatever it takes” to push the Rwanda plan through, and said he would explore similar arrangements with other countries. Other parts of his immigration agenda laid out to Conservative Party voters included capping the annual number of refugees Britain accepted and cutting foreign aid to countries that decline to accept failed asylum seekers trying to enter the U.K.

For her part, Ms. Truss called for “full implementation” of the Rwanda plan and also said she would solicit other countries willing to take in British illegal immigrants. She also called for an increase in staffing for the country’s Border Force to better police the English Channel for small boats making the dangerous voyage to try to reach British soil.

She also told the Mail on Sunday newspaper she would not “cower” before critics and human rights activists who say the policy is inhumane and would force many migrants to relocate to a country where they had never been.

The Johnson government in May announced a plan with Rwanda’s government to relocate failed asylum seekers to the east African country permanently, but the first flights this summer were scrubbed following a furious legal battle over the policy. Britain was to pay Rwanda roughly $150 million initially for economic development and for the expenses to settle the refugees.

Amnesty International was one of the rights groups that have harshly condemned the plan.

“By trying to dump asylum seekers in Rwanda, the U.K. government is shirking its international responsibility under the Refugee Convention to protect people in need of asylum,” Deprose Muchena, Amnesty international’s director for East and Southern Africa, said in a statement last month, calling on the Johnson government to “rescind its misguided, cruel and racist policy that shifts its responsibility towards refugees and asylum seekers to Rwanda.”