The World Health Organization (WHO) has told the BBC that medical supplies are urgently needed in several places including the worst-hit city of Derna and will "need to scale up very, very urgently".
Rick Brennan, the WHO's emergency director for the Eastern Mediterranean region which includes Libya, said many health facilities had not been functioning well even before the storm.
"A large proportion of those health facilities were already poorly stocked, poorly staffed," he said.
The WHO, he said, was in a position to lead the collaborative efforts of other aid agencies but that was being delayed because of Libya's two governments in the west and the east.
There were issues around getting clearance from the government to get aid going to where it was needed, he noted.
"Most of the early response to any big crisis like this is done by the local community... but we... the international community, we need to come in behind them and provide the support at scale that's proportionate to these massive needs," he said.