"It is the duty of the government of Syria to want to reach every Syrian person wherever they are and allow the UN to bring humanitarian aid," Mr de Mistura said after talks in Damascus on Tuesday.
"Tomorrow we test this."
The Syrian government of President Bashar al-Assad earlier approved humanitarian access to seven areas which are besieged, either by government troops or rebel groups.
The areas are those deemed by the 17-member International Syria Support Group to be most in need of relief.
Almost half a million people live in besieged areas, according to the UN.
The cessation of hostilities - which does not apply to jihadist groups - is due to come into force later this week.
But President Assad has cast doubts on the move, warning it would be "difficult" to implement and would not mean all parties would stop using weapons.
His forces, backed by Russian air power, have been advancing in the north and threaten to surround the key city of Aleppo.
Where the aid is going
The seven areas named by the UN are:
Deir el-Zour, a city in the east under siege from so-called Islamic State
Foah and Kefraya, in northern Idlib province, besieged by rebels
Madaya, Muadhamiya, Kafr Batna and Zabadani, all in the Damascus area under siege from government forces
Earlier this week, Russia said it "categorically rejects" accusations of war crimes over the bombing of hospitals in Syria.
Turkey has blamed Russia for a series of rocket attacks on several hospitals and schools that killed up to 50 people.
But Kremlin spokesman Dmitry Peskov told the BBC that the only proof Russia would accept from the ground "comes from the Syrian authorities".
Save the Children has said that seven healthcare facilities were hit by strikes on Monday - more than previously reported.
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