His statement came after UN chief Ban Ki-moon issued a report saying that foreign aid was still not reaching millions of needy Syrians despite a Security Council resolution in February calling for greater access.
Ban's report last week blamed both sides in the war but singled out the government for particular censure.
On Saturday state television broadcast footage showing Assad in a meeting with representatives of Syria's governmental relief committee.
"There is a need for greater cooperation between ministries and the bodies involved in humanitarian aid, and to deliver aid without delay, and to work on the ground with all the local and international stakeholders to make aid delivery smoother," he said.
Assad's statement came three days after UN humanitarian chief Valerie Amos said Resolution 2139 was not working.
Referring to the wars in Bosnia and Somalia, Amos said the Council would need to pass a number of different resolutions under Chapter VII of the UN Charter to get the required humanitarian access.
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Chapter VII provides for binding resolutions enforceable through sanctions or the use of military force. Any such resolution would meet with stiff opposition from Russia, a key backer of the Assad regime, and China.
International legal experts have also demanded action, and called on the United Nations to deliver aid from Jordan and Turkey via border crossings controlled by rebels.
But Assad's regime has so far blocked any efforts to allow international aid to be taken into opposition-held areas through the crossings, and his latest statement gave no indication that policy had changed.
Instead, he said aid delivery must improve "without compromising national sovereignty."
"The state is responsible for covering the needs of all its citizens... not only in the areas where they have fled to (and which are in government control) but also in the areas under siege by the terrorists," he said.
Damascus refers to opposition activists and armed rebels as "terrorists," and blames them for the violence engulfing Syria.