Bring to shore the 160 rescued people who have been aboard two Captain Morgan vessels for weeks, the UN Refugee Agency and International Organisation for Migration urged on Thursday.
They called on Malta and other European states to "speed efforts" in bringing the asylum seekers to "dry land and safety".
A separate group of 21 people, mostly families, women and children, have already been evacuated and disembarked in Malta several days ago, they added.
"It is important to disembark the remaining people as soon as possible, as they have been on board the vessel for some two weeks - the standard quarantine period for COVID-19 - without any clarity on disembarkation. It is unacceptable to leave people at sea longer than necessary, especially under difficult and unsuitable conditions."
Malta shut its ports to asylum seekers, citing the COVID-19 pandemic, in April.
It has since returned one group of migrants to Libya through the intervention of a private fishing boat and hosted other groups aboard the cruise boats, for which it is paying €3,000 a day each to lease.
On Tuesday NGO Alarm Phone claimed that migrants aboard the cruise vessels at sea had started a hunger strike.
In a statement earlier on Wednesday, the government said that Malta has received just two offers from all other EU member states to take in migrants this year.
On Thursday UNHCR and IOM said Mediterranean states have been at the forefront of receiving sea arrivals in recent years.
Their efforts, and those of NGO search and rescue vessels, have prevented many tragic deaths, they added.
However, UNHCR and IOM were also deeply concerned about reports that states have been ignoring or delaying responses to distress calls, especially amid a sharp decrease in state led and NGO search and rescue capacity.
"We remind states of their obligations under international law to immediately assist people in distress. These obligations cannot be traded away with the offer of fuel and aid. States must take every effort to promptly rescue people in distress, as a delay of even a few minutes could make the difference between life and death."
'Public health measures must be applied without discrimination'
Public health measures such as mandatory, time-limited quarantines, medical screening and physical distancing must be applied without discrimination and within the specified national health protocol.
States must continue to disembark people rescued at sea, in line with international maritime law obligations and ensure access to asylum and humanitarian assistance, the two said in a statement.
Acknowledging that reception capacities in some Mediterranean states were further challenged by necessary health measures put in place due to COVID-19, UNHCR and IOM have offered support to ensure the effective and speedy processing of new arrivals.
Prompt disembarkation must also be supported by tangible solidarity from other European states through a timely and predictable relocation mechanism and – once conditions permit – effective cooperation on returns to country of origin for those found not to be in need of international protection.
"A clearly agreed system for post-disembarkation relocation is urgently needed if we are to finally move away from a perpetual cycle of negotiations and ad-hoc arrangements that put the lives and health of people at further risk.
"The relocation of 17 people on Wednesday from Malta to France shows that solidarity at the time of COVID-19 is possible, with all necessary precautions and measures to ensure preventing further spreading of the virus in place."
UNHCR and IOM reiterated that no one rescued at sea should be returned to Libya.
Direct or indirect State involvement through commercial boats in the return of rescued migrants and refugees to Libya may constitute a violation of international law, the added.
Treatment of people at sea not worthy of people of Malta - HRW
In another statement early on Friday, Human Rights Watch said it is incredible that the Maltese government would hold these people captive on tourist ferries in miserable conditions for weeks to pressure other EU countries to take them,” acting deputy Europe and Central Asia director at Human Rights Watch Judith Sunderland said.
“Concerns about Covid-19 and long-standing complaints, in part justified, about lack of fair sharing of responsibility can’t excuse this disgraceful behaviour.”
It said EU states should not only relocate this group and follow through on prior commitments, but also strongly condemn the Maltese authorities for the arbitrary deprivation of liberty of scores of people and the violations of the law of the sea and of EU asylum standards, and urge Malta to allow the people to disembark.
The European Commission should also open infringement proceedings against Malta for violating its EU treaty obligations.
“We believe the 160 people on board tourist cruise boats on the high sea are experiencing severe emotional and physical distress but we don’t believe their treatment, and violation of their rights, is worthy of the people of Malta, or any EU country,” Sunderland said.