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.
Both sides so far appear unwilling to compromise. The Iranian New Year this week and campaigning for the country's presidential election in June are also likely to complicate matters.
"Iran must make the expected gestures and behave in a responsible way," Macron added.
Macron and Le Pen would easily qualify for the runoff after picking up about 25% each in the first round scheduled for April 2022, far ahead of other rivals. Macron would go on to defeat Le Pen with 53% of the votes versus 47%.
"Centre-left voters are disappointed, that's for sure," one minister, speaking on condition of anonymity, told Reuters.
"I stand in solidarity with the three countries that have had their diplomats expelled," Macron told a news conference following a virtual meeting of the France-German Defence and Security Council.
It said Macron told a media briefing that included the Saudi-owned channel that a very short time remained to prevent Iran from having a nuclear weapon.