Rudd Lubbers, head of the UNHCR agency, warned the EU was in danger of breaking international law and the UN Convention on Refugees.
He also warned that the recently established asylum systems in the 10 new member states could be overwhelmed by illegal immigrants.
He said the EU should share the burden of looking after asylum seekers and provide extra support for the 10 countries that join in May.
"If we are not careful, we risk overwhelming fragile and under-resourced asylum systems in the new EU states," Mr Lubbers said.
However, Mr McDowell, chairing a meeting of fellow EU Justice Ministers in Dublin, said they had to deal with the realities of the situation.
"I understand he is keen to maintain the 1951 Convention, but member states have to deal with the practicalities and take practical steps to deal with the realities," he said.
He agreed there might be a difference in the way the ministers and the UN interpreted the Convention on Refugees and the EU would follow its own legal advice. "Different people have different understandings of international law and there is not a single, sole interpretation of it," he said.
The UN is concerned at the EU's attempt to draw up a list of minimum conditions people must fulfil before any EU country will recognise them as refugees. This is an effort to prevent asylum seekers shopping around for an easy country to enter.
Mr Lubbers said there was a danger this would become a catalogue of optional provisions, including some that would depart from international refugee and human rights law.
The EU will enforce the so-called Dublin Two in relation to the new member states, a system which, in effect, means asylum seekers will be sent back to the first European country they entered to have their application processed.
With asylum seekers being fingerprinted they can now be more easily identified if they move from state to state and can be sent back to the first state they entered most likely the new members that will form Europe's new borders.
"A decade ago they had no asylum systems at all. What is going to happen if thousands of extra asylum-seekers are sent back to them from the inner EU countries? There is a danger the harmonized procedures may simply collapse in the new border states leading to more instead of less irregular movement between EU states," said Mr Lubbers.
He presented the ministers with a set of proposals that would ensure the burden would be equally shared among all the members. This would include reception centres with assessors and interpreters drawn from across the EU, sharing them out among all the countries and an EU Asylum Agency to manage the new systems.
However, Germany's Foreign Minister, Otto Schily, believed that once the new members join they should fund the asylum problems in their own territory.
"The EU has given a lot of support to the new member states but now they are inside the EU they have to meet the obligations," he said.
The European Ministers want to draw up a list of countries they consider are safe so that people coming from them cannot claim to be seeking asylum from persecution. They could be refused entry at the border.
Mr McDowell said that rather than start on a list of safe countries they would first decide on how to define a safe country.
He did not believe that Russia would qualify as a safe place to send Chechens.
The deadline for agreeing the new proposals is May 1.
Mr McDowell said the ministers had made good progress at yesterday's meeting and hope to meet the deadline. The meeting continues today.