EU foreign policy chief Federica Mogherini has pleaded for UN help to dismantle criminal groups smuggling migrants into the European Union.
"We need to count on your support to save lives," she told a Security Council briefing on EU plans to use force against smugglers.
Libya, where many smugglers operate, has objected to the EU proposals.
More than 1,800 migrants have died in the Mediterranean in 2015 - a 20-fold increase on the same period in 2014.
Some 60,000 people have already tried to make the perilous crossing this year, the UN estimates.
Many are fleeing conflict or poverty in countries such as Syria, Eritrea, Nigeria and Somalia.
Analysis: Gavin Lee, BBC News, Brussels
This was a speech aimed at rallying nations outside of the EU to galvanise their wider support in tackling the migrant crisis. It was also an attempt to determine a legal basis for the search-and-destroy operations to be carried out on empty, Libyan, smuggling boats.
But the difficulty lies in telling the difference between a fishing boat and a trafficker's vessel, whilst at the same time ensuring the safety of migrants. The ways to achieve this are still being deliberated. EU officials tell me the approach they are considering is "unorthodox, and something that hasn't been tried before".
The complexities are expected to be worked out by next week, which is why the UN speech was relevant - any military plan will need to work in accordance with international law. Diplomats are said to be drafting a resolution which will need to be agreed by the five permanent members of the UN Security Council: Britain, France, China, Russia and the US.
Considering the strained international relations between Moscow and the West, it will take an extraordinary act of unity for this operation to go ahead.
'No-one sent back against will'
Speaking in New York on Monday, Ms Mogherini said the EU's first priority was to "save lives and prevent further loss of lives at sea".
She outlined proposals agreed by EU governments last month, including the "use of all necessary means to seize and dispose of the vessels".
The EU must seek UN approval in order to establish a clear legal basis for any military operation to seize smugglers' boats in Libyan territorial waters.
Diplomats from Italy, the UK, France, Lithuania and Spain are drafting a UN Security Council resolution under chapter seven of the UN charter that endorses the EU's migrant crisis plan, with the aim of getting a mandate for the use of force to maintain international peace.
It is as yet unclear what shape military action could take.
Earlier, the Libyan ambassador to the UN told the BBC that the EU's intentions were unclear and that the Libyan government had not yet been consulted.
Ms Mogherini told UN representatives on Monday that an "exceptional response" was needed to deal with the "unprecedented" migrant flow.
But she said the situation was likely to continue as long as Libya lacked a government that had authority across the country.
"No refugees or migrants intercepted at sea will be sent back against their will," she added.
Military approach criticised
Ms Mogherini travelled to Beijing last week to try to build support for a draft resolution, amid concerns that China and Russia would veto the proposal to use military force.
UN Secretary General Ban Ki-moon has cautioned against a military solution. Rights groups, including Amnesty International, are also warning that military action could leave migrants trapped in Libya in desperate conditions.
As part of the EU plan, the European Commission is expected to propose a quota system for distributing asylum seekers between its members on Wednesday. It will also introduce plans to increase legal means for migrants to come to Europe so that they do not turn to smugglers.
Countries most affected by the crisis, including Italy, Malta, Austria and Greece, are urging EU members to share the responsibility for migrants more evenly.
A quota system would need to be agreed by EU states and is highly controversial, with many countries fiercely opposed.
While Germany and France support the idea, leaders in the UK, Hungary, Slovakia and Estonia have voiced their objections.
Proposals agreed by EU nations to deal with the migrant crisis in April include:
- reinforcing search and rescue efforts
- tripling financial resources for this purpose over the next two years
- disrupting smuggling networks and bringing the perpetrators to justice
- efforts to identify, capture and destroy their vessels