"This new site is currently functioning as an emergency shelter facility," UNHCR spokesperson Shabia Mantoo said in Geneva.
"UNHCR supports its use as temporary solution but cautions that what may be deemed adequate in terms of shelter and services during emergency situations is not appropriate for the longer-term."
Hundreds of asylum seekers including elderly people and small children were queueing on Friday to enter the coastal tent camp, which was hastily built to replace Europe's largest camp of Moria that burned down on September 8.
Six young Afghans have been arrested in connection with the fire.
Moria was notoriously overcrowded and unsanitary, and its destruction has strengthened calls for the migrants to be moved off the island from both local residents and humanitarian organisations.
"Greek authorities are yet to clarify the future use of (the new) site. We stand ready to support discussions on possible long-term solutions, including the continuation of safe and orderly transfers to the mainland and EU-supported relocations," Mantoo said.
A migration ministry spokesman said some 6,000 people had entered the camp since the relocation operation began this week.
Among them, 157 have tested positive for the novel coronavirus, he said.
The UN refugee agency in Geneva said it was "assisting with site planning and mapping to facilitate the shelter allocation, provision of information and distribution of relief items for all those who enter the site."
"We understand the operation proceeds smoothly and no use of force or incidents of violence were reported," the agency said.
Some reporters have complained of police obstruction whilst covering the relocation operation this week. One said he was handcuffed and thrown to the ground by police.
"Refugees seem relieved to have found basic assistance but still worn-out from being on the street for several days and worried about the future," UNHCR said.
Many asylum seekers have told AFP that they are wary of entering the new camp, or are doing so out of necessity as they are no longer able to sleep on the street with limited access to food and water.
Greek Prime Minister Kyriakos Mitsotakis on Friday said he had discussed a "new, permanent facility" to be built on Lesbos with European Commission chief Ursula von der Leyen and German Chancellor Angela Merkel via teleconference.
Athens has said it wants the EU to adopt a more active role in managing the new camp.