Some four million people in the rebel-held northwest rely on humanitarian aid.
The Syrian government said on Friday it had approved the delivery of humanitarian aid to areas outside its control in the quake-hit rebel-held northwest of the country.
"The Council of Ministers approves... the delivery of humanitarian aid to all parts of the Syrian Arab Republic," a cabinet statement said.
It added that aid distribution should be supervised by the International Committee of the Red Cross (ICRC) and the Syrian Red Crescent with UN help.
"Any initiative that contributes to alleviating the suffering of civilians is welcome," ICRC's regional director Fabrizio Carboni told AFP after the decision.
"The ICRC welcome any steps that would lead to delivering much-needed aid to people faster."
ICRC chief Mirjana Spoljaric visited Syria's quake-damaged Aleppo city on Friday.
Monday's massive quake killed more than 22,700 people in Turkey and Syria, in one of the region's worst disasters in a century.
The United Nations routinely delivers aid to rebel-held areas, either from neighbouring Turkey through the Bab al-Hawa crossing or directly across the front line from government-held areas.
Some four million people in the rebel-held northwest rely on humanitarian aid, but there have been no aid deliveries from government-controlled areas in three weeks.
Only two aid convoys have reached the region this week from Turkey, where authorities are engaged in an even bigger quake relief operation of their own.
UN chief Antonio Guterres urged the Security Council on Thursday to authorise the opening of additional crossings on the Turkey-Syria border for the delivery of UN aid to quake victims in rebel areas.
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