The pair are to meet on Friday at the Commonwealth Heads of Government Meeting (Chogm) summit in the African country, where the prime minister initially told reporters he would explain the “obvious merits” of the plan to the heir to the throne.
But Downing Street later backed away from the promise, saying it was “unlikely” Johnson would mention the scheme, which involves flying asylum-seekers who cross the Channel in small boats to Rwanda without first assessing their claim for sanctuary in the UK.
No 10 also said the PM did not raise the issue of human rights in talks with Rwandan president Paul Kagame, despite a slew of reports of political repression, alleged assassinations and the imprisonment of critics.
Mr Johnson insisted that the east African nation had undergone an “absolute transformation” and said it was “condescending” to oppose plans forcibly to relocate asylum-seekers there.
The scheme was roundly condemned at the parliamentary assembly of the Council of Europe by MPs from across the continent who described it as “unethical” and “racist”.
Plans for the first flight were halted at the last minute last week by rulings from the European Court of Human Rights and the UK’s Appeal Court, and further attempts to fly migrants out are not likely to be made until after a judicial review next month.
But No 10 said that the policy would not be “at the forefront of his mind” when Mr Johnson joins the Prince for talks over a cup of tea, in their first conversation since reports of the Charles’s private remarks. It was understood that the Prince is also unlikely to bring it up.
Despite being in Rwanda for the first time since becoming PM, Mr Johnson was not expected to visit the facilities set up to receive “tens of thousands” of asylum-seekers from the UK once the scheme gets under way.
The government in Kigali said it had already received payments under a £120 million economic and migration deal signed by home secretary Priti Patel two months ago, and some of the money had already been spent.
Rwandan government spokeswoman Yolande Makolo said: “Because that was intended to prepare for all the accommodations and all the other institutions to beef up the processes – so that’s been done.”
A Downing Street account of talks between Mr Johnson and Mr Kagame suggested that the pair were trying to claim success for the scheme, despite the fact that no migrants have yet been removed from the UK.
A No 10 spokesman said: “The leaders also praised the successful UK-Rwanda Migration and Economic Development Partnership, which is tackling dangerous smuggling gangs while offering people a chance to build a new life in a safe country.”
Mr Johnson defended the scheme, which has been described by Church of England bishops as bringing “shame” on Britain.
Speaking to reporters as he prepared to fly to Rwanda, the PM said he hoped the trip would “perhaps help others to shed some of their condescending attitudes to Rwanda and how that partnership might work”.
And speaking to broadcasters during a visit to a school in Kigali, he said: “People need to keep an open mind about the policy, the critics need to keep an open mind about the policy.
“A lot of people can see its obvious merits. So yeah, of course, if I am seeing the prince tomorrow, I am going to be making that point.”
Mr Johnson said he found it “utterly shocking” to see evidence of the 1994 genocide of 800,000 Tutsis and moderate Hutus at a memorial in Kigali.
“We must do everything we can to ensure that human hearts never again are allowed to breed such hatred,” he said.