BEIRUT, Lebanon — The ferocious ground assault and aerial bombardment in eastern Aleppo has forced some 16,000 people to flee for their lives in the last few days, according to Stephen O’Brien, the United Nations under secretary general for humanitarian affairs.

“The parties to the conflict have shown time and again they are willing to take any action to secure military advantage even if it means killing, maiming or starving civilians into submission in the process,” Mr. O’Brien warned on Tuesday, calling the siege of the city a “deeply alarming and chilling situation.”

On Monday, forces loyal to President Bashar al-Assad captured about a third of the territory in Aleppo that had been held by rebels. Planes have dropped leaflets over the rebel-held areas in the eastern part of city. “If you don’t leave these areas quickly you will be annihilated,” the leaflets warn. “Save yourselves. You know that everyone has left you alone to face your doom and have offered you no help.”

Hisham al-Skeif, a member of a council of rebels and civilians in eastern Aleppo, said by telephone on Tuesday that warplanes had hovered closely over the area, steadily dropping barrel bombs, as a delegation of civic activists explored the idea of using so-called safe routes to leave the city, though many were not confident they could escape with their lives.