Peter Maurer told AFP in an interview that his organization had distributed food and other urgent aid items to more than 1.5 million people last year, and had helped 17 million Syrians access safe water.
Yet, "this is insufficient compared to the negative impact of this conflict on the civilian population. We would like to do much more," he said, lamenting that there were a number of places in Syria out of reach to most aid workers.
According to United Nations figures, more than 60,000 people have been killed since the revolt against President Bashar al-Assad's regime began in March 2011, while some 730,000 Syrians have fled to neighbouring countries.
"Nowhere else in the world is there an armed conflict that is as unpredictable within such large boundaries and affecting as many people," said Maurer, who visited Damascus last September, just months after he took over the helm of the ICRC.
"Our ambition is to continue to expand the surface we cover in Syria, and I really hope we can do more tomorrow and the day after," Maurer said, calling on all parties in the conflict to help the ICRC and other aid workers "reach the people we have to reach."
The most important thing for his organization, he said, was "that all parties of the conflict respect the role of the ICRC (and) respect the special protection of medical facilities, of ambulances and doctors and nurses."
Since his three-day visit to Syria and meetings with Assad last September, Maurer said the Syrian president had kept some of his promises of increased access and the ICRC had noticed some improvements.
Yet other promises had not been kept, he said, without specifying which ones.
He stressed that he did "not want to go to Syria before we have some assurances that progress will be made" or before the regime gave him the green light to travel beyond Damascus.
"In light of the current situation, I cannot go to Syria if I am not able to travel to other regions of Syria," he said.