"Europe has provided financial support, but more is needed. It has to continue; it has to be probably more substantive," United Nations High Commissioner for Refugees (UNHCR) Filippo Grandi told reporters in Athens.
The Dublin Regulation, which dictates that the first country in which an asylum seeker applies for asylum is responsible for accepting or rejecting the claim, is completely inadequate, said Grandi.
"Europe has to have a new system that is based more on responsibility-sharing," he said.
Greece is facing a new refugee crisis as there has been a dramatic hike in asylum seekers this year, with reception centers on Aegean Sea islands overflowing with new arrivals.
So far in 2019, more than 60,000 people have arrived in Greece overland and by sea, according to the latest report by the UNHCR.
Current conditions in refugee camps on the island of Lesvos are "extremely disturbing," with inadequate access to basic services and a situation of general tension that often results in violence, Grandi said on a visit to Greece.
The UN official urged Athens to improve living conditions in refugee camps, ease overcrowding by moving refugees to the mainland, ensure a fair asylum process and protect unaccompanied children.