BEIRUT, Lebanon — An array of groups allied with the Syrian government pressed an assault on rebel-held eastern Aleppo on Friday, as the World Health Organization said heavy bombardment of the area by Russia and Syria had killed 338 people in the last week, including more than 100 children.

With more of the city’s already limited hospitals destroyed in the latest offensive, Dr. Richard Brennan, the organization’s director of emergency response, told reporters that many of the 846 people wounded were expected to die for lack of treatment. That includes 261 children, he said.

There were competing claims about the success of the government’s offensive on Friday, with the government saying its fighters had captured more territory in northern parts of the city and penetrated the center of Aleppo, where they were clashing with the rebels.

Rebel commanders denied the reports, however, saying government forces had not made any progress since capturing the Handarat refugee camp north of the city on Thursday.