BEIRUT (Reuters) - The Syrian army sent text messages to residents of rebel-held eastern Aleppo saying it will grant safe passage to people wishing to leave the area, which has been effectively besieged by pro-government forces, state media said on Tuesday.

The army called on residents to push "mercenaries" out of the city -- a reference to rebel fighters -- and said it would give safe passage and temporary accommodation for anyone wishing to leave the area, state news agency SANA said.

The messages also called on armed groups to lay down their weapons, SANA said.

Concern has been growing for at least 250,000 people who have been trapped in rebel-held eastern Aleppo since heavy fighting effectively closed the last supply route, the Castello Road, in early July.

Syria's most populous city before the war, Aleppo has been divided for years between rebel and government-held zones. Full control of Aleppo would be a significant prize for President Bashar al-Assad.

On Monday, Russia's U.N. Ambassador Vitaly Churkin told the U.N. Security Council that by day people in the eastern areas of Aleppo can move to the western part of the city, "where the situation is significantly better".

Churkin's comments came in a session during which the United Nations aid chief asked the Security Council to push for a weekly 48-hour humanitarian pause in fighting to allow food and other aid to be delivered to eastern areas of the city.

(Reporting by Lisa Barrington; Editing by Catherine Evans)