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The rebel-held east of Syria's Aleppo has officially been declared a "besieged area", following a months-long government offensive and a lack of access for aid workers, the UN said on Wednesday.

Eastern Aleppo will now be "included automatically in the monthly plans for access either through cross-border deliveries or cross-line deliveries," United Nations humanitarian agency (OCHA) spokesperson Jens Laerke said.

It now meets all three criteria used to define an area as besieged, he explained. 

The criteria include military encirclement, lack of humanitarian access and the lack of free movement for civilians.

The UN and Red Cross have been pushing to get aid into eastern Aleppo for weeks, but those efforts have been stalled by insecurity and bureaucratic problems, including obstacles imposed by both the Damascus government and rebel commanders.

Eastern Aleppo has replaced Daraya on the list, after the latter town was emptied of residents and opposition fighters under a deal with the government.

The west of the city is controlled by the government and has continued to receive relief supplies. 

Once Syria's economic powerhouse, Aleppo has been devastated by the country's brutal five-year civil war, with the suffering intensifying since regime troops cut off the last supply route in July.

There are now 18 besieged areas in Syria, according to the UN.

Eastern Aleppo now meets all three criteria used to define an area as besieged: military encirclement, lack of humanitarian access and the lack of free movement for civilians.

On Wednesday, the UN estimated that half of the estimated 275,000 Syrians besieged in eastern Aleppo want to leave, as food supplies are running thin and people are driven to burning plastic for fuel.

"An assessment conducted in eastern Aleppo city concluded that 50 percent of the inhabitants expressed willingness to leave if they can," OCHA said in an update on the Aleppo situation.

"Moreover, arguments among spouses have reportedly increased as many women are blaming their husbands for choosing to stay while it was possible to leave the city."

Aid workers in eastern Aleppo have distributed food rations for 13,945 children under 6 years old, but a lack of cooking gas makes it difficult to cook what little food remains.

"Reports of civilians rummaging through the rubble of destroyed buildings to salvage any flammable material that can be used for cooking are common," the report said.

Agencies contributed to this report.