In the past, health workers have been abducted in the region, which has has seen the heaviest fighting between the Taliban and international forces.
But a Taliban spokesman, has said that the vaccinators would be allowed access in southern Afghanistan for the current campaign.
"We will fully help the vaccination teams to carry out their campaign and they will not to be hurt by anyone as all our friends have been told to provide a safe environment for the vaccinators," he said, according to Unicef.
The vaccinators had not been able to work in parts of Helmand province for about 18 months, Mbengue said.
"This is an incredible, happy development."
About 10,000 volunteer vaccinators began the campaign on Wednesday, aiming to vaccinate 1.3 million children in 10 provinces.
The vaccinators finished three days of work in the south and east on Friday, and will continue in western Farah province for three more days beginning on Monday.
Mbengue said that on International Peace Day, which was held on Friday, "we were able to see that vaccination was taking place all over the country".
Afghanistan is one of just four countries that still suffers endemic polio, the others are Pakistan, India and Nigeria.
Mbengue said there had been nine polio cases in Afghanistan this year, all of them in the south and east. Last year there were 29 cases, 21 of them in the south.
Polio mainly affects children under the age of five. It is spread when unvaccinated people come into contact with the faeces of those with the virus, often through water.
It usually attacks the nervous system, causing paralysis, muscular atrophy, deformation and sometimes death.