Conditions for refugees in Greece are worsening and arrival numbers rising but the safeguards needed to start returning some of them to Turkey next week are not yet in place, aid agencies said.
Fighting has broken out in some crowded reception centres in Greece, which now hosts 51,000 refugees and migrants.
The system for registering asylum applications is overloaded, the UN High Commissioner for Refugees (UNHCR) said.
Turkey is due to begin taking back illegal migrants from Greece on Monday under a deal with the European Union, but neither side is fully ready and any start may only be symbolic.
UNHCR, which says nine in ten of refugees arriving on rickety boats are fleeing for their lives, has voiced concern that Turkey may deport refugees en masse to Afghanistan, Iran and Iraq, where they could face persecution or violence.
"We are urging parties to the recent EU-Turkey agreement on refugees and migrants to ensure all safeguards are in place before any returns begin," UNHCR spokeswoman Melissa Fleming told a Geneva news briefing.
"This is in light of continued serious gaps in both countries."
UNHCR wants to keep track of those returned to Turkey to ensure that standards of international protection for refugees and migrants are upheld, she said.
"UNHCR has requested access to people returned from Greece to ensure (they) can benefit from effective international protection and prevent risk of ... forcible return," she said.
Arrivals in Greece picked up this week amid better weather.
At least 170,000 people entered Europe by sea in the first three months of 2016, over eight times that in the same period last year, the International Organisation for Migration (IOM) said.
"There seems to be no sign of the migrant surge slowing down," IOM spokesman Joel Millman said, noting increased traffic between Libya and Italy.
Some 89 people are now feared to have died in a shipwreck on Wednesday off Libya, which 31 survived, he said.
Fleming reported worsening conditions on the Greek islands of Lesbos and Samos - where three people were stabbed in rioting last night - and at the Athens port of Piraeus and Idomeni at the border with Macedonia.
"The risk of panic and injury in these sites and others is real," Ms Fleming said, citing further incidents of fighting.
The UNHCR is monitoring conditions at a facility at Moria, on Lesbos, where 2,300 are being held. "People are sleeping in the open and the food supply is insufficient," she said.
The EU must provided greater support, as promised, to boost Greece's creaking asylum system, Ms Fleming added.