"Our security guarantees remain in place", he said.
It follows a pause in Syrian government air strikes overnight, with the situation in the besieged enclave on Friday described as "calm".
A previous delivery of aid to the region was cut short amid shelling. Moscow supports the government of Bashar al-Assad in Syria.
A rebel fighter with Jaish al-Islam, one of the main factions in eastern Ghouta, said intense fighting was underway.
All U.N. vehicles and OCHA staff should be allowed to enter the biggest eastern Ghouta town of Douma on Thursday with the medical supplies that were removed on Monday, and without their vehicles being subjected to inspections, he said.
Reports were sketchy and it was not immediately clear if the ICRC had offloaded all the aid.
The 13 truckloads are part of the former 46 trucks that entered Douma a few days before but couldn't be unloaded at the time due to the situation on the ground, Sedky said.
MSF said there was an acute emergency in Eastern Ghouta, where nearly 400,000 civilians have endured a blistering military assault by the Syrian government and its allies since February 18.
Syria's regime sent reinforcements to Eastern Ghouta yesterday, tightening the noose around the shrinking rebel enclave ahead of a top-level U.N. meeting on the escalating violence.The blistering onslaught has prompted outrage against the regime, with the United Nations' human rights chief saying the government was orchestrating an "apocalypse" in Syria.
The working class towns and farming villages of the East Ghouta suburbs are home to an estimated 400,00 residents.
As a result of the violence a Red Cross convoy due to carry aid into the besieged district on Thursday was cancelled, with aid workers unable to say when it would get through. "Everything has been used up, and Ghouta has nothing".
Another 60 were left struggling to breathe after a suspected chlorine gas attack in the Hammuriyeh area.
There was no confirmation by any of the rebel groups based in eastern Ghouta of negotiations to leave eastern Ghouta.
At least 100 residents displayed symptoms of chlorine gas inhalation, the spokesman added.
Reuters could not independently verify the images or claims.
In 2017, World Health Organization counted 112 attacks on Syrian healthcare facilities and medical workers.
The trucks were instead parked on the edges of eastern Ghouta, at the government-controlled Wafideen checkpoint, Agence France-Presse reported.
Government forces this week advanced from the east and were only about two kilometres away from linking with forces on the western side of Eastern Ghouta.