The EU's 27 leaders were unable to agree on migration policy reforms on Friday, after a two-day summit that was unexpectedly extended as Hungary and Poland made a last-minute request for a majority-backed deal to be reopened.
European Council President Charles Michel issued a separate statement on migration, which said that Hungary and Poland rejected the obligation for EU countries to share the hosting of asylum seekers.
EU home affairs ministers agreed on June 8 on a migration pact, which requires compulsory help between EU members. The vote was done by a qualified majority, with Poland and Hungary voting against the proposals, while Bulgaria, Malta, Lithuania and Slovakia abstained.
But Polish Prime Minister Mateusz Morawiecki said that he would not yield on the issue, accusing EU partners of wanting the migrant-sharing deal "to be a forced process, not a voluntary process".
Hungarian Prime Minister Viktor Orban told state radio: "We can only accept any rule if all of us agree on it, if there is a unanimous decision."
Mr Michel's statement noted that Hungary and Poland declared that "relocation and resettlement should be on a voluntary basis."
The two countries also requested that decisions on migration be adopted by unanimity and not by qualified majority as required by EU treaties. This would give them veto power.
The bloc's remaining 25 member states do not share this point of view, Mr Michel said.
Poland and Hungary disagree on the migration pact's content and disapprove its decision process, he said, "because these two countries have a different interpretation of previous conclusions of the European Council."
Their objection has no impact on negotiations moving forward on the migration deal at the level of the European Parliament.
"The migration pact has been validated and it will be implemented," said Mr Michel.
The issuance of separate conclusions on migration by Mr Michel is widely viewed as an attempt by most EU countries to show their support to the pact despite Hungary and Poland's objections.
Some leaders expressed their disappointment. EU leaders had initially come to a general agreement on migration by Thursday evening.
As he arrived at the summit's second day on Friday morning, Irish Prime Minister Leo Varadkar indicated that he was unconvinced by the necessity of continuing discussions on migration.
"I'm not sure we needed another meeting about it again," he told reporters.
Poland and Hungary "don’t want to be told to take migrants, but we take a view that there has to be burden sharing and there has to be solidarity," he said.
Poland would have been happy with a change of wording in the conclusions but Hungary staunchly rejected it, added Mr Varadkar.
"One thing for sure is that we’re going to see a lot of irregular migration into Europe over the summer," said the Irish Prime Minister. "This issue is going to grow."
Poland has long opposed any relocation of migrants - usually from Africa, Asia and the Middle East - who arrived in Greece or Italy first.
The Polish government wants a national referendum on the question of welcoming refugees.
Deaths of migrants at sea have continued dominating headlines in Europe with the recent drowning of at least 500 people, mostly from Pakistan, Egypt and Syria, off the Greek coast on June 13.
Investigative news website Lighthouse Reports on Friday accused Greece of tampering with evidence after survivors said that the boast capsised because Greek coastguards towed the fishing ship with a rope.
Some think tanks in Brussels interpreted Mr Morawiecki and Mr Orban's objections as political posturing ahead of EU elections next year.
"It's all for show," tweeted Camino Mortero, head of the Centre for European Reform.
