Regime backer Russian Federation last week announced daily five-hour "humanitarian pauses" in Eastern Ghouta.
Meanwhile, a group monitoring the conflict on the ground in Ghouta reported fresh casualties from the bombing campaign.
The Syrian regime has taken control of several villages in the rebel-held enclave of Eastern Ghouta, official news agency SANA said Sunday, in a major turning point in a two-week offensive.
OCHA said the aid would be taken in to Eastern Ghouta by the United Nations and its partners, after they "received approval to deliver assistance for 70,000 people in need in the besieged enclave".
The Observatory and the Syrian Civil Defense said civilians had fled their homes because of the advancing troops, with many of them were taking cover in underground shelters.
On Saturday, 18 civilians, including three children, were killed in government bombardment of Eastern Ghouta, according to the Observatory.
The oppositional Syrian Observatory for Human Rights said the government forces' bombardment and airstrikes on Eastern Ghouta have killed over 600 people since the situation started flaring last month.
Also on Sunday, British Prime Minister Theresa May's office said she and US President Donald Trump discussed the "heart-breaking human suffering" in Syria, pinning the blame on the Assad regime and Russian Federation.
French President Emmanuel Macron made a separate phone call to Iranian President Hassan Rouhani urging him to exert "necessary pressure" on Syria to halt "indiscriminate" attacks on civilians in Eastern Ghouta.
The UN said in a statement it has received approval to carry medicine and food for 27,000 people in the region, but claim they have not be able to go into the region to provide aid. In a statement, it accused Syrian President Bashar al-Assad and Russian Federation of waging a "scorched earth" campaign.
Referring to the daily five-hour truce, which the United States has dismissed as a "joke", Assad said there was "no contradiction between a truce and combat operations".
In a statement released Sunday, the UN's Office for the Coordination of Humanitarian Affairs said it hoped to deliver aid to parts of the area on Monday.
The UN's regional humanitarian coordinator for Syria, Panos Moumtzis, sounded the alarm on Sunday over the increase in violence.
Mr Rahman also said 26 of the people killed were in Ghouta's main town of Douma and its eastern suburb.
The UN says an unacceptable "collective punishment" is being meted out to the 350,000 people thought still to live in the area, which was one of the first to host protests against the regime in March 2011.
"Instead of a much-needed reprieve, we continue to see more fighting, more death, and more disturbing reports of hunger and hospitals being bombed", he said in a statement.