UNHCR issued the strongly-worded statement after more than 300 migrants were feared drowned this week when their overcrowded dinghies sank, the latest boat tragedy in a perilous crossing from Africa to Europe.
"UNHCR is today calling on the European Union to urgently change its approach to dealing with sea crossings with a view to ensuring that saving lives is the top-most priority," it said.
The latest deaths have highlighted the limited means and scope of Triton, an EU-run mission which took over in November from the Italian navy's Mare Nostrum search and rescue operation.
Italy decided to scale back the mission after its EU partners refused to share running costs of around nine million euros ($10 million) a month.
Triton, which comes under the authority of the EU borders agency Frontex, has a monthly budget of 2.9 million euros ($3.3 million) and its patrols are generally restricted to the territorial waters of EU member states.
"There can be no doubt left after this week's events that Europe's Operation Triton is a woefully inadequate replacement for Italy's Mare Nostrum," said UN High Commissioner for Refugees Antonio Guterres.
"The focus has to be about saving lives," Guterres said.
"We need a robust search and rescue operation in the Central Mediterranean, not only a border patrol."
Guterres said he is concerned that Europe is planning to phase out rather than step up its rescue efforts in response to the growing boat disasters.
UNHCR said at least 3,500 people lost their lives last year out of more than 218,000 migrants who crossed the Mediterranean, making it the most deadly route in the world.
The surge in migrants is a result of wars, conflicts and poverty in Syria, the Horn of Africa and other parts of sub-Saharan Africa.