Downing Street said Johnson "outlined his intention to host a virtual meeting... in the coming days", during a call to French President Emmanuel Macron when he stressed the need for a "unified approach" to the situation.
Macron and South Africa President Cyril Ramaphosa will hold talks and then head to the University of Pretoria to launch a programme to support African vaccine production, a project backed by the European Union, United States and World Bank.
The president tweeted that as his flight took off for Kigali, he felt "a deep conviction: over the coming hours, together we will write a new chapter in our relations with Rwanda and Africa".
"Someone at the start of the 21st century does not think like someone at the start of the 19th century," he said. "Our history is our history and we accept it."
Credit insurer Euler Hermes estimates that the EU is now seven weeks adrift of its target to have 70 percent of the population vaccinated by the end of the summer, compared with five weeks in February.