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Previously, the two countries were outvoted in favor of a plan to divide migrants arriving in Europe among the 27 member states.
AP reported that Poland and Hungary refused to support the summit statement, which requires unanimity.
Belgian Prime Minister Alexandre de Croo told reporters that they were left with two options: Either the migration talks would continue, or they would give up and say there would be no joint statement at the summit.
There is a clear willingness among most countries to try to reach an agreement, said De Croo.
Negotiations will continue later today at a summit in Brussels.
Ahead of the meeting in Brussels, Polish Prime Minister Mateusz Morawiecki insisted Poland would not be forced to accept EU rules on migration and announced he would veto any plan that could force countries to take in migrants.
"The attack on Europe is underway. European borders are not safe. The safety of the inhabitants of our continent is at stake," Morawiecki said in a video statement.
Morawiecki announced that he would propose a "plan for secure borders" to EU leaders.
Earlier this month, EU interior ministers adopted an agreement on a responsibility-sharing plan for migrants entering Europe illegally.
Under that agreement, countries that refuse to accept migrants can instead pay 20,000 euros per person.
The agreement was signed by a qualified majority of around two-thirds, and only Poland and Hungary voted against it.
Poland, Hungary, and the Czech Republic have refused to accept migrant quotas that the EU urgently imposed in 2015, when more than a million people, mostly Syrians fleeing the war, entered Europe.
The EU High Court ruled in 2020 that those countries did not respect the laws of the Union.