The delivery of aid to Syria's rebel-held Eastern Ghouta has been "postponed", the Red Cross has said, as Syrian government forces stepped up their offensive against rebels in the enclave.

An aid convoy was scheduled to reach the besieged area on Thursday, and aimed to deliver much needed medical supplies that were prevented from being delivered earlier this week.

On Wednesday, members of the United Nations Security Council called for the immediate implementation of a resolution it had passed on February 24, which demanded a 30-day ceasefire in Syria.

Netherlands ambassador to the UN, Karel van Oosterom, said in a statement that members of the council "expressed concern" about the humanitarian situation, and reiterated calls for the implementation of resolution 2401 during a closed meeting.

UN human rights chief Zeid Raad al-Hussein said the government's offensive, backed by Russia, was creating an "apocalypse".

Since February 18, Russian-backed government warplanes intensified their bombardment of Eastern Ghouta.

The government has been fighting armed opposition groups in the Damascus suburb from multiple fronts, and said on Tuesday it will send reinforcements to join the battle.

A pro-government Syrian military commander told Reuters news agency on Thursday that the army managed to slice the enclave into two, as forces advance from the east.

However, a spokesperson of one of the rebel groups in the enclave denied the claim.

Wael Olwan, of the Failaq al-Rahman (the Rahman Legion), a major armed group linked to the Free Syrian Army in Eastern Ghouta, told Al Jazeera on Wednesday that Assad forces have only attained about 30 percent of land.

"Assad's forces advanced near the town of Beit Siwa, while rebels have taken new positions in Al Muhammadiyah," he said. "The battles are ongoing and face-to-face fighting comes and goes, it's not ongoing."

According to Mahmoud Adam, spokesperson for Syria's Civil Defence, also known as the White Helmets, at least 50 people were killed on Wednesday as a result of government shelling and artillery fire.

"They [government forces] have not left anything but used it against the people of Ghouta - from phosphorus bomb attacks to artillery fire," he told Al Jazeera.

To date, at least 800 people have been killed since the start of the latest offensive, SOHR reported.

The Damascus suburb has been under rebel control since mid-2013. Shortly after, Syrian President Bashar al-Assad imposed a siege on the area, home to some 400,000 people.

The ongoing confrontation has forced many of the residents to leave their towns on the outskirts of Eastern Ghouta, opting to flee deeper into the rebel-controlled enclave.

At least 1,000 families left their homes for the central city of Douma on Tuesday and Wednesday, despite a Russian-sponsored truce that pledged to create "humanitarian corridors" last week.

In an attempt to alleviate the dire humanitarian crisis in Eastern Ghouta, a 46-truck convoy managed to enter the enclave for the first time in weeks on Monday.

However, Syrian authorities prevented at least 14 of the trucks from unloading surgical supplies and medicine, resulting in the delivery of only half of the aid meant for about 27,000 residents.