KANDAHAR, Afghanistan — Shahwalikot, a district in southern Afghanistan that is largely controlled by the Taliban, has the sad distinction of being the polio capital of the world. Four new cases have been reported there this year, out of 20 worldwide — the indirect consequence of a war that is also killing and maiming children in increasingly large numbers.

On Monday, vaccinators began another dangerous attempt to immunize children in Shahwalikot, as the United Nations urgently appealed to all sides of the conflict to let them work. But after a day of going door to door and village to village in Shahwalikot, in Kandahar Province, they had gained access to just three of the 28 zones they needed to reach. They said the Taliban had promised to eventually let them into 11 others.

Pleading for cooperation before the immunization campaign began, Toby Lanzer, the United Nations humanitarian coordinator for Afghanistan, said the surge in polio cases in Shahwalikot had the potential to ultimately put hundreds of thousands of Afghan children at risk.

“In the past days, yet another case of wild poliovirus was found,” Mr. Lanzer said. “The outbreak of polio in Shahwalikot means that Afghanistan remains one of only three countries in the world that is still polio-endemic, and polio eradication is at risk globally. This week’s campaign in Kandahar is more important than ever.”