WASHINGTON — Already grappling with divisions in his own country over vaccine mandates and questions about the ethics and efficacy of booster shots, President Biden is facing another front of discord: a split among world leaders over how to eradicate the coronavirus globally, as the highly infectious Delta variant leaves a trail of death in its wake.

At a virtual summit on Wednesday, while the annual United Nations General Assembly meeting is underway, Mr. Biden will try to persuade other vaccine-producing countries to balance their domestic needs with a renewed focus on manufacturing and distributing doses to poor nations in desperate need of them.

Covax, the United Nations-backed vaccine program, is so far behind schedule that not even 10 percent of the population in poor nations is fully vaccinated, experts said.